Global Stability Results for Switched Systems Based on Weak Lyapunov Functions
In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbation-like one. Most stability results for perturbed systems are based on the use of strong...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Mancilla-Aguilar, Jose L [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2017 |
|---|
| Schlagwörter: |
|---|
| Übergeordnetes Werk: |
Enthalten in: IEEE transactions on automatic control - New York, NY : Inst., 1963, 62(2017), 6, Seite 2764-2777 |
|---|---|
| Übergeordnetes Werk: |
volume:62 ; year:2017 ; number:6 ; pages:2764-2777 |
| Links: |
|---|
| DOI / URN: |
10.1109/TAC.2016.2627622 |
|---|
| Katalog-ID: |
OLC199400231X |
|---|
| LEADER | 01000caa a2200265 4500 | ||
|---|---|---|---|
| 001 | OLC199400231X | ||
| 003 | DE-627 | ||
| 005 | 20210716194507.0 | ||
| 007 | tu | ||
| 008 | 170721s2017 xx ||||| 00| ||eng c | ||
| 024 | 7 | |a 10.1109/TAC.2016.2627622 |2 doi | |
| 028 | 5 | 2 | |a PQ20171125 |
| 035 | |a (DE-627)OLC199400231X | ||
| 035 | |a (DE-599)GBVOLC199400231X | ||
| 035 | |a (PRQ)c1352-8730f01e56cd6ebd9da252c717ff5a7b54095d4810619097493747369d04bd10 | ||
| 035 | |a (KEY)0005057120170000062000602764globalstabilityresultsforswitchedsystemsbasedonwea | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | 4 | |a 620 |q DNB |
| 100 | 1 | |a Mancilla-Aguilar, Jose L |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Global Stability Results for Switched Systems Based on Weak Lyapunov Functions |
| 264 | 1 | |c 2017 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a ohne Hilfsmittel zu benutzen |b n |2 rdamedia | ||
| 338 | |a Band |b nc |2 rdacarrier | ||
| 520 | |a In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbation-like one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-time-varying. We provide two types of ISS results: standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm. | ||
| 650 | 4 | |a nonlinear dynamical systems | |
| 650 | 4 | |a Switches | |
| 650 | 4 | |a Nonlinear systems | |
| 650 | 4 | |a Lyapunov methods | |
| 650 | 4 | |a Asymptotic stability | |
| 650 | 4 | |a Standards | |
| 650 | 4 | |a time-varying systems | |
| 650 | 4 | |a Switched systems | |
| 650 | 4 | |a input-to-state stability | |
| 700 | 1 | |a Haimovich, Hernan |4 oth | |
| 700 | 1 | |a Garcia, Rafael A |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |t IEEE transactions on automatic control |d New York, NY : Inst., 1963 |g 62(2017), 6, Seite 2764-2777 |w (DE-627)129601705 |w (DE-600)241443-0 |w (DE-576)015095320 |x 0018-9286 |7 nnns |
| 773 | 1 | 8 | |g volume:62 |g year:2017 |g number:6 |g pages:2764-2777 |
| 856 | 4 | 1 | |u http://dx.doi.org/10.1109/TAC.2016.2627622 |3 Volltext |
| 856 | 4 | 2 | |u http://ieeexplore.ieee.org/document/7740968 |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_OLC | ||
| 912 | |a SSG-OLC-TEC | ||
| 912 | |a SSG-OLC-MAT | ||
| 912 | |a GBV_ILN_11 | ||
| 912 | |a GBV_ILN_70 | ||
| 912 | |a GBV_ILN_120 | ||
| 912 | |a GBV_ILN_193 | ||
| 912 | |a GBV_ILN_2014 | ||
| 912 | |a GBV_ILN_2016 | ||
| 912 | |a GBV_ILN_2333 | ||
| 912 | |a GBV_ILN_4193 | ||
| 951 | |a AR | ||
| 952 | |d 62 |j 2017 |e 6 |h 2764-2777 | ||
| author_variant |
j l m a jlm jlma |
|---|---|
| matchkey_str |
article:00189286:2017----::lbltbltrslsosicessesaeowa |
| hierarchy_sort_str |
2017 |
| publishDate |
2017 |
| allfields |
10.1109/TAC.2016.2627622 doi PQ20171125 (DE-627)OLC199400231X (DE-599)GBVOLC199400231X (PRQ)c1352-8730f01e56cd6ebd9da252c717ff5a7b54095d4810619097493747369d04bd10 (KEY)0005057120170000062000602764globalstabilityresultsforswitchedsystemsbasedonwea DE-627 ger DE-627 rakwb eng 620 DNB Mancilla-Aguilar, Jose L verfasserin aut Global Stability Results for Switched Systems Based on Weak Lyapunov Functions 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbation-like one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-time-varying. We provide two types of ISS results: standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm. nonlinear dynamical systems Switches Nonlinear systems Lyapunov methods Asymptotic stability Standards time-varying systems Switched systems input-to-state stability Haimovich, Hernan oth Garcia, Rafael A oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 6, Seite 2764-2777 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:6 pages:2764-2777 http://dx.doi.org/10.1109/TAC.2016.2627622 Volltext http://ieeexplore.ieee.org/document/7740968 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 62 2017 6 2764-2777 |
| spelling |
10.1109/TAC.2016.2627622 doi PQ20171125 (DE-627)OLC199400231X (DE-599)GBVOLC199400231X (PRQ)c1352-8730f01e56cd6ebd9da252c717ff5a7b54095d4810619097493747369d04bd10 (KEY)0005057120170000062000602764globalstabilityresultsforswitchedsystemsbasedonwea DE-627 ger DE-627 rakwb eng 620 DNB Mancilla-Aguilar, Jose L verfasserin aut Global Stability Results for Switched Systems Based on Weak Lyapunov Functions 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbation-like one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-time-varying. We provide two types of ISS results: standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm. nonlinear dynamical systems Switches Nonlinear systems Lyapunov methods Asymptotic stability Standards time-varying systems Switched systems input-to-state stability Haimovich, Hernan oth Garcia, Rafael A oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 6, Seite 2764-2777 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:6 pages:2764-2777 http://dx.doi.org/10.1109/TAC.2016.2627622 Volltext http://ieeexplore.ieee.org/document/7740968 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 62 2017 6 2764-2777 |
| allfields_unstemmed |
10.1109/TAC.2016.2627622 doi PQ20171125 (DE-627)OLC199400231X (DE-599)GBVOLC199400231X (PRQ)c1352-8730f01e56cd6ebd9da252c717ff5a7b54095d4810619097493747369d04bd10 (KEY)0005057120170000062000602764globalstabilityresultsforswitchedsystemsbasedonwea DE-627 ger DE-627 rakwb eng 620 DNB Mancilla-Aguilar, Jose L verfasserin aut Global Stability Results for Switched Systems Based on Weak Lyapunov Functions 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbation-like one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-time-varying. We provide two types of ISS results: standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm. nonlinear dynamical systems Switches Nonlinear systems Lyapunov methods Asymptotic stability Standards time-varying systems Switched systems input-to-state stability Haimovich, Hernan oth Garcia, Rafael A oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 6, Seite 2764-2777 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:6 pages:2764-2777 http://dx.doi.org/10.1109/TAC.2016.2627622 Volltext http://ieeexplore.ieee.org/document/7740968 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 62 2017 6 2764-2777 |
| allfieldsGer |
10.1109/TAC.2016.2627622 doi PQ20171125 (DE-627)OLC199400231X (DE-599)GBVOLC199400231X (PRQ)c1352-8730f01e56cd6ebd9da252c717ff5a7b54095d4810619097493747369d04bd10 (KEY)0005057120170000062000602764globalstabilityresultsforswitchedsystemsbasedonwea DE-627 ger DE-627 rakwb eng 620 DNB Mancilla-Aguilar, Jose L verfasserin aut Global Stability Results for Switched Systems Based on Weak Lyapunov Functions 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbation-like one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-time-varying. We provide two types of ISS results: standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm. nonlinear dynamical systems Switches Nonlinear systems Lyapunov methods Asymptotic stability Standards time-varying systems Switched systems input-to-state stability Haimovich, Hernan oth Garcia, Rafael A oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 6, Seite 2764-2777 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:6 pages:2764-2777 http://dx.doi.org/10.1109/TAC.2016.2627622 Volltext http://ieeexplore.ieee.org/document/7740968 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 62 2017 6 2764-2777 |
| allfieldsSound |
10.1109/TAC.2016.2627622 doi PQ20171125 (DE-627)OLC199400231X (DE-599)GBVOLC199400231X (PRQ)c1352-8730f01e56cd6ebd9da252c717ff5a7b54095d4810619097493747369d04bd10 (KEY)0005057120170000062000602764globalstabilityresultsforswitchedsystemsbasedonwea DE-627 ger DE-627 rakwb eng 620 DNB Mancilla-Aguilar, Jose L verfasserin aut Global Stability Results for Switched Systems Based on Weak Lyapunov Functions 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbation-like one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-time-varying. We provide two types of ISS results: standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm. nonlinear dynamical systems Switches Nonlinear systems Lyapunov methods Asymptotic stability Standards time-varying systems Switched systems input-to-state stability Haimovich, Hernan oth Garcia, Rafael A oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 6, Seite 2764-2777 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:6 pages:2764-2777 http://dx.doi.org/10.1109/TAC.2016.2627622 Volltext http://ieeexplore.ieee.org/document/7740968 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 62 2017 6 2764-2777 |
| language |
English |
| source |
Enthalten in IEEE transactions on automatic control 62(2017), 6, Seite 2764-2777 volume:62 year:2017 number:6 pages:2764-2777 |
| sourceStr |
Enthalten in IEEE transactions on automatic control 62(2017), 6, Seite 2764-2777 volume:62 year:2017 number:6 pages:2764-2777 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| topic_facet |
nonlinear dynamical systems Switches Nonlinear systems Lyapunov methods Asymptotic stability Standards time-varying systems Switched systems input-to-state stability |
| dewey-raw |
620 |
| isfreeaccess_bool |
false |
| container_title |
IEEE transactions on automatic control |
| authorswithroles_txt_mv |
Mancilla-Aguilar, Jose L @@aut@@ Haimovich, Hernan @@oth@@ Garcia, Rafael A @@oth@@ |
| publishDateDaySort_date |
2017-01-01T00:00:00Z |
| hierarchy_top_id |
129601705 |
| dewey-sort |
3620 |
| id |
OLC199400231X |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a2200265 4500</leader><controlfield tag="001">OLC199400231X</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20210716194507.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">170721s2017 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1109/TAC.2016.2627622</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">PQ20171125</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC199400231X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)GBVOLC199400231X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(PRQ)c1352-8730f01e56cd6ebd9da252c717ff5a7b54095d4810619097493747369d04bd10</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(KEY)0005057120170000062000602764globalstabilityresultsforswitchedsystemsbasedonwea</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">620</subfield><subfield code="q">DNB</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Mancilla-Aguilar, Jose L</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Global Stability Results for Switched Systems Based on Weak Lyapunov Functions</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2017</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbation-like one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-time-varying. We provide two types of ISS results: standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">nonlinear dynamical systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Switches</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nonlinear systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lyapunov methods</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Asymptotic stability</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Standards</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">time-varying systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Switched systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">input-to-state stability</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Haimovich, Hernan</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Garcia, Rafael A</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">IEEE transactions on automatic control</subfield><subfield code="d">New York, NY : Inst., 1963</subfield><subfield code="g">62(2017), 6, Seite 2764-2777</subfield><subfield code="w">(DE-627)129601705</subfield><subfield code="w">(DE-600)241443-0</subfield><subfield code="w">(DE-576)015095320</subfield><subfield code="x">0018-9286</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:62</subfield><subfield code="g">year:2017</subfield><subfield code="g">number:6</subfield><subfield code="g">pages:2764-2777</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">http://dx.doi.org/10.1109/TAC.2016.2627622</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">http://ieeexplore.ieee.org/document/7740968</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-TEC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_120</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_193</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2016</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2333</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4193</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">62</subfield><subfield code="j">2017</subfield><subfield code="e">6</subfield><subfield code="h">2764-2777</subfield></datafield></record></collection>
|
| author |
Mancilla-Aguilar, Jose L |
| spellingShingle |
Mancilla-Aguilar, Jose L ddc 620 misc nonlinear dynamical systems misc Switches misc Nonlinear systems misc Lyapunov methods misc Asymptotic stability misc Standards misc time-varying systems misc Switched systems misc input-to-state stability Global Stability Results for Switched Systems Based on Weak Lyapunov Functions |
| authorStr |
Mancilla-Aguilar, Jose L |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)129601705 |
| format |
Article |
| dewey-ones |
620 - Engineering & allied operations |
| delete_txt_mv |
keep |
| author_role |
aut |
| collection |
OLC |
| remote_str |
false |
| illustrated |
Not Illustrated |
| issn |
0018-9286 |
| topic_title |
620 DNB Global Stability Results for Switched Systems Based on Weak Lyapunov Functions nonlinear dynamical systems Switches Nonlinear systems Lyapunov methods Asymptotic stability Standards time-varying systems Switched systems input-to-state stability |
| topic |
ddc 620 misc nonlinear dynamical systems misc Switches misc Nonlinear systems misc Lyapunov methods misc Asymptotic stability misc Standards misc time-varying systems misc Switched systems misc input-to-state stability |
| topic_unstemmed |
ddc 620 misc nonlinear dynamical systems misc Switches misc Nonlinear systems misc Lyapunov methods misc Asymptotic stability misc Standards misc time-varying systems misc Switched systems misc input-to-state stability |
| topic_browse |
ddc 620 misc nonlinear dynamical systems misc Switches misc Nonlinear systems misc Lyapunov methods misc Asymptotic stability misc Standards misc time-varying systems misc Switched systems misc input-to-state stability |
| format_facet |
Aufsätze Gedruckte Aufsätze |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
nc |
| author2_variant |
h h hh r a g ra rag |
| hierarchy_parent_title |
IEEE transactions on automatic control |
| hierarchy_parent_id |
129601705 |
| dewey-tens |
620 - Engineering |
| hierarchy_top_title |
IEEE transactions on automatic control |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 |
| title |
Global Stability Results for Switched Systems Based on Weak Lyapunov Functions |
| ctrlnum |
(DE-627)OLC199400231X (DE-599)GBVOLC199400231X (PRQ)c1352-8730f01e56cd6ebd9da252c717ff5a7b54095d4810619097493747369d04bd10 (KEY)0005057120170000062000602764globalstabilityresultsforswitchedsystemsbasedonwea |
| title_full |
Global Stability Results for Switched Systems Based on Weak Lyapunov Functions |
| author_sort |
Mancilla-Aguilar, Jose L |
| journal |
IEEE transactions on automatic control |
| journalStr |
IEEE transactions on automatic control |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
600 - Technology |
| recordtype |
marc |
| publishDateSort |
2017 |
| contenttype_str_mv |
txt |
| container_start_page |
2764 |
| author_browse |
Mancilla-Aguilar, Jose L |
| container_volume |
62 |
| class |
620 DNB |
| format_se |
Aufsätze |
| author-letter |
Mancilla-Aguilar, Jose L |
| doi_str_mv |
10.1109/TAC.2016.2627622 |
| dewey-full |
620 |
| title_sort |
global stability results for switched systems based on weak lyapunov functions |
| title_auth |
Global Stability Results for Switched Systems Based on Weak Lyapunov Functions |
| abstract |
In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbation-like one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-time-varying. We provide two types of ISS results: standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm. |
| abstractGer |
In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbation-like one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-time-varying. We provide two types of ISS results: standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm. |
| abstract_unstemmed |
In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbation-like one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-time-varying. We provide two types of ISS results: standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm. |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 |
| container_issue |
6 |
| title_short |
Global Stability Results for Switched Systems Based on Weak Lyapunov Functions |
| url |
http://dx.doi.org/10.1109/TAC.2016.2627622 http://ieeexplore.ieee.org/document/7740968 |
| remote_bool |
false |
| author2 |
Haimovich, Hernan Garcia, Rafael A |
| author2Str |
Haimovich, Hernan Garcia, Rafael A |
| ppnlink |
129601705 |
| mediatype_str_mv |
n |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| author2_role |
oth oth |
| doi_str |
10.1109/TAC.2016.2627622 |
| up_date |
2024-07-03T16:06:41.330Z |
| _version_ |
1803574628929503232 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a2200265 4500</leader><controlfield tag="001">OLC199400231X</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20210716194507.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">170721s2017 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1109/TAC.2016.2627622</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">PQ20171125</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC199400231X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)GBVOLC199400231X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(PRQ)c1352-8730f01e56cd6ebd9da252c717ff5a7b54095d4810619097493747369d04bd10</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(KEY)0005057120170000062000602764globalstabilityresultsforswitchedsystemsbasedonwea</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">620</subfield><subfield code="q">DNB</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Mancilla-Aguilar, Jose L</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Global Stability Results for Switched Systems Based on Weak Lyapunov Functions</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2017</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbation-like one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-time-varying. We provide two types of ISS results: standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">nonlinear dynamical systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Switches</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nonlinear systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lyapunov methods</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Asymptotic stability</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Standards</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">time-varying systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Switched systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">input-to-state stability</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Haimovich, Hernan</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Garcia, Rafael A</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">IEEE transactions on automatic control</subfield><subfield code="d">New York, NY : Inst., 1963</subfield><subfield code="g">62(2017), 6, Seite 2764-2777</subfield><subfield code="w">(DE-627)129601705</subfield><subfield code="w">(DE-600)241443-0</subfield><subfield code="w">(DE-576)015095320</subfield><subfield code="x">0018-9286</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:62</subfield><subfield code="g">year:2017</subfield><subfield code="g">number:6</subfield><subfield code="g">pages:2764-2777</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">http://dx.doi.org/10.1109/TAC.2016.2627622</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">http://ieeexplore.ieee.org/document/7740968</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-TEC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_120</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_193</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2016</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2333</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4193</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">62</subfield><subfield code="j">2017</subfield><subfield code="e">6</subfield><subfield code="h">2764-2777</subfield></datafield></record></collection>
|
| score |
7.3980513 |