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
Autor*in: |
Mancilla-Aguilar, Jose L [verfasserIn] |
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Englisch |
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2017 |
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Enthalten in: IEEE transactions on automatic control - New York, NY : Inst., 1963, 62(2017), 6, Seite 2764-2777 |
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Übergeordnetes Werk: |
volume:62 ; year:2017 ; number:6 ; pages:2764-2777 |
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DOI / URN: |
10.1109/TAC.2016.2627622 |
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Katalog-ID: |
OLC199400231X |
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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 | |
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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 |
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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 |
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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 |
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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 |
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Enthalten in IEEE transactions on automatic control 62(2017), 6, Seite 2764-2777 volume:62 year:2017 number:6 pages:2764-2777 |
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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. 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Global Stability Results for Switched Systems Based on Weak Lyapunov Functions |
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Global Stability Results for Switched Systems Based on Weak Lyapunov Functions |
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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. |
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Global Stability Results for Switched Systems Based on Weak Lyapunov Functions |
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