Summation Inequalities to Bounded Real Lemmas of Discrete-Time Systems With Time-Varying Delay
Summation inequality is an important technique for analysis of discrete-time systems with a time-varying delay. It seems that from the literature a tighter inequality usually leads to a less conservative criterion. Based on <inline-formula><tex-math notation="LaTeX">H_{\infty}&...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Zhang, Chuan-Ke [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: IEEE transactions on automatic control - New York, NY : Inst., 1963, 62(2017), 5, Seite 2582-2588 |
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| Übergeordnetes Werk: |
volume:62 ; year:2017 ; number:5 ; pages:2582-2588 |
| Links: |
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| DOI / URN: |
10.1109/TAC.2016.2600024 |
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| Katalog-ID: |
OLC1991838344 |
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| 520 | |a Summation inequality is an important technique for analysis of discrete-time systems with a time-varying delay. It seems that from the literature a tighter inequality usually leads to a less conservative criterion. Based on <inline-formula><tex-math notation="LaTeX">H_{\infty}</tex-math></inline-formula> performance analysis problem, this note presents different findings on the relationship between the conservatism of bounded real lemma (BRL) and the tightness of summation inequality. Firstly, the BRL obtained by the Wirtinger-based inequality (WBI) is not always less conservative than the one by the Jensen-based inequality although the WBI is tighter. Secondly, the WBI is tighter than a general free-matrix-based inequality (GFMBI) developed in this note, while the BRL obtained via the GFMBI is less conservative than the WBI-based BRL. Finally, a numerical example is given to demonstrate those findings. | ||
| 650 | 4 | |a summation inequality | |
| 650 | 4 | |a bounded real lemma | |
| 650 | 4 | |a Discrete-time system | |
| 650 | 4 | |a Time-varying systems | |
| 650 | 4 | |a Automation | |
| 650 | 4 | |a Discrete-time systems | |
| 650 | 4 | |a Performance analysis | |
| 650 | 4 | |a Symmetric matrices | |
| 650 | 4 | |a time-varying delay | |
| 650 | 4 | |a Linear matrix inequalities | |
| 650 | 4 | |a Delays | |
| 700 | 1 | |a He, Yong |4 oth | |
| 700 | 1 | |a Jiang, Lin |4 oth | |
| 700 | 1 | |a Wu, Min |4 oth | |
| 700 | 1 | |a Zeng, Hong-Bing |4 oth | |
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10.1109/TAC.2016.2600024 doi PQ20170501 (DE-627)OLC1991838344 (DE-599)GBVOLC1991838344 (PRQ)c704-435429b3f782886fc2ff6381c9d8e78943c76bb02ff86a8932548a35f87bc68c0 (KEY)0005057120170000062000502582summationinequalitiestoboundedreallemmasofdiscrete DE-627 ger DE-627 rakwb eng 620 DNB Zhang, Chuan-Ke verfasserin aut Summation Inequalities to Bounded Real Lemmas of Discrete-Time Systems With Time-Varying Delay 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Summation inequality is an important technique for analysis of discrete-time systems with a time-varying delay. It seems that from the literature a tighter inequality usually leads to a less conservative criterion. Based on <inline-formula><tex-math notation="LaTeX">H_{\infty}</tex-math></inline-formula> performance analysis problem, this note presents different findings on the relationship between the conservatism of bounded real lemma (BRL) and the tightness of summation inequality. Firstly, the BRL obtained by the Wirtinger-based inequality (WBI) is not always less conservative than the one by the Jensen-based inequality although the WBI is tighter. Secondly, the WBI is tighter than a general free-matrix-based inequality (GFMBI) developed in this note, while the BRL obtained via the GFMBI is less conservative than the WBI-based BRL. Finally, a numerical example is given to demonstrate those findings. summation inequality bounded real lemma Discrete-time system Time-varying systems Automation Discrete-time systems Performance analysis Symmetric matrices time-varying delay Linear matrix inequalities Delays He, Yong oth Jiang, Lin oth Wu, Min oth Zeng, Hong-Bing oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 5, Seite 2582-2588 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:5 pages:2582-2588 http://dx.doi.org/10.1109/TAC.2016.2600024 Volltext http://ieeexplore.ieee.org/document/7542509 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 5 2582-2588 |
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10.1109/TAC.2016.2600024 doi PQ20170501 (DE-627)OLC1991838344 (DE-599)GBVOLC1991838344 (PRQ)c704-435429b3f782886fc2ff6381c9d8e78943c76bb02ff86a8932548a35f87bc68c0 (KEY)0005057120170000062000502582summationinequalitiestoboundedreallemmasofdiscrete DE-627 ger DE-627 rakwb eng 620 DNB Zhang, Chuan-Ke verfasserin aut Summation Inequalities to Bounded Real Lemmas of Discrete-Time Systems With Time-Varying Delay 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Summation inequality is an important technique for analysis of discrete-time systems with a time-varying delay. It seems that from the literature a tighter inequality usually leads to a less conservative criterion. Based on <inline-formula><tex-math notation="LaTeX">H_{\infty}</tex-math></inline-formula> performance analysis problem, this note presents different findings on the relationship between the conservatism of bounded real lemma (BRL) and the tightness of summation inequality. Firstly, the BRL obtained by the Wirtinger-based inequality (WBI) is not always less conservative than the one by the Jensen-based inequality although the WBI is tighter. Secondly, the WBI is tighter than a general free-matrix-based inequality (GFMBI) developed in this note, while the BRL obtained via the GFMBI is less conservative than the WBI-based BRL. Finally, a numerical example is given to demonstrate those findings. summation inequality bounded real lemma Discrete-time system Time-varying systems Automation Discrete-time systems Performance analysis Symmetric matrices time-varying delay Linear matrix inequalities Delays He, Yong oth Jiang, Lin oth Wu, Min oth Zeng, Hong-Bing oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 5, Seite 2582-2588 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:5 pages:2582-2588 http://dx.doi.org/10.1109/TAC.2016.2600024 Volltext http://ieeexplore.ieee.org/document/7542509 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 5 2582-2588 |
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10.1109/TAC.2016.2600024 doi PQ20170501 (DE-627)OLC1991838344 (DE-599)GBVOLC1991838344 (PRQ)c704-435429b3f782886fc2ff6381c9d8e78943c76bb02ff86a8932548a35f87bc68c0 (KEY)0005057120170000062000502582summationinequalitiestoboundedreallemmasofdiscrete DE-627 ger DE-627 rakwb eng 620 DNB Zhang, Chuan-Ke verfasserin aut Summation Inequalities to Bounded Real Lemmas of Discrete-Time Systems With Time-Varying Delay 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Summation inequality is an important technique for analysis of discrete-time systems with a time-varying delay. It seems that from the literature a tighter inequality usually leads to a less conservative criterion. Based on <inline-formula><tex-math notation="LaTeX">H_{\infty}</tex-math></inline-formula> performance analysis problem, this note presents different findings on the relationship between the conservatism of bounded real lemma (BRL) and the tightness of summation inequality. Firstly, the BRL obtained by the Wirtinger-based inequality (WBI) is not always less conservative than the one by the Jensen-based inequality although the WBI is tighter. Secondly, the WBI is tighter than a general free-matrix-based inequality (GFMBI) developed in this note, while the BRL obtained via the GFMBI is less conservative than the WBI-based BRL. Finally, a numerical example is given to demonstrate those findings. summation inequality bounded real lemma Discrete-time system Time-varying systems Automation Discrete-time systems Performance analysis Symmetric matrices time-varying delay Linear matrix inequalities Delays He, Yong oth Jiang, Lin oth Wu, Min oth Zeng, Hong-Bing oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 5, Seite 2582-2588 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:5 pages:2582-2588 http://dx.doi.org/10.1109/TAC.2016.2600024 Volltext http://ieeexplore.ieee.org/document/7542509 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 5 2582-2588 |
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10.1109/TAC.2016.2600024 doi PQ20170501 (DE-627)OLC1991838344 (DE-599)GBVOLC1991838344 (PRQ)c704-435429b3f782886fc2ff6381c9d8e78943c76bb02ff86a8932548a35f87bc68c0 (KEY)0005057120170000062000502582summationinequalitiestoboundedreallemmasofdiscrete DE-627 ger DE-627 rakwb eng 620 DNB Zhang, Chuan-Ke verfasserin aut Summation Inequalities to Bounded Real Lemmas of Discrete-Time Systems With Time-Varying Delay 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Summation inequality is an important technique for analysis of discrete-time systems with a time-varying delay. It seems that from the literature a tighter inequality usually leads to a less conservative criterion. Based on <inline-formula><tex-math notation="LaTeX">H_{\infty}</tex-math></inline-formula> performance analysis problem, this note presents different findings on the relationship between the conservatism of bounded real lemma (BRL) and the tightness of summation inequality. Firstly, the BRL obtained by the Wirtinger-based inequality (WBI) is not always less conservative than the one by the Jensen-based inequality although the WBI is tighter. Secondly, the WBI is tighter than a general free-matrix-based inequality (GFMBI) developed in this note, while the BRL obtained via the GFMBI is less conservative than the WBI-based BRL. Finally, a numerical example is given to demonstrate those findings. summation inequality bounded real lemma Discrete-time system Time-varying systems Automation Discrete-time systems Performance analysis Symmetric matrices time-varying delay Linear matrix inequalities Delays He, Yong oth Jiang, Lin oth Wu, Min oth Zeng, Hong-Bing oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 5, Seite 2582-2588 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:5 pages:2582-2588 http://dx.doi.org/10.1109/TAC.2016.2600024 Volltext http://ieeexplore.ieee.org/document/7542509 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 5 2582-2588 |
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10.1109/TAC.2016.2600024 doi PQ20170501 (DE-627)OLC1991838344 (DE-599)GBVOLC1991838344 (PRQ)c704-435429b3f782886fc2ff6381c9d8e78943c76bb02ff86a8932548a35f87bc68c0 (KEY)0005057120170000062000502582summationinequalitiestoboundedreallemmasofdiscrete DE-627 ger DE-627 rakwb eng 620 DNB Zhang, Chuan-Ke verfasserin aut Summation Inequalities to Bounded Real Lemmas of Discrete-Time Systems With Time-Varying Delay 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Summation inequality is an important technique for analysis of discrete-time systems with a time-varying delay. It seems that from the literature a tighter inequality usually leads to a less conservative criterion. Based on <inline-formula><tex-math notation="LaTeX">H_{\infty}</tex-math></inline-formula> performance analysis problem, this note presents different findings on the relationship between the conservatism of bounded real lemma (BRL) and the tightness of summation inequality. Firstly, the BRL obtained by the Wirtinger-based inequality (WBI) is not always less conservative than the one by the Jensen-based inequality although the WBI is tighter. Secondly, the WBI is tighter than a general free-matrix-based inequality (GFMBI) developed in this note, while the BRL obtained via the GFMBI is less conservative than the WBI-based BRL. Finally, a numerical example is given to demonstrate those findings. summation inequality bounded real lemma Discrete-time system Time-varying systems Automation Discrete-time systems Performance analysis Symmetric matrices time-varying delay Linear matrix inequalities Delays He, Yong oth Jiang, Lin oth Wu, Min oth Zeng, Hong-Bing oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 5, Seite 2582-2588 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:5 pages:2582-2588 http://dx.doi.org/10.1109/TAC.2016.2600024 Volltext http://ieeexplore.ieee.org/document/7542509 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 5 2582-2588 |
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| author |
Zhang, Chuan-Ke |
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Zhang, Chuan-Ke ddc 620 misc summation inequality misc bounded real lemma misc Discrete-time system misc Time-varying systems misc Automation misc Discrete-time systems misc Performance analysis misc Symmetric matrices misc time-varying delay misc Linear matrix inequalities misc Delays Summation Inequalities to Bounded Real Lemmas of Discrete-Time Systems With Time-Varying Delay |
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620 DNB Summation Inequalities to Bounded Real Lemmas of Discrete-Time Systems With Time-Varying Delay summation inequality bounded real lemma Discrete-time system Time-varying systems Automation Discrete-time systems Performance analysis Symmetric matrices time-varying delay Linear matrix inequalities Delays |
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ddc 620 misc summation inequality misc bounded real lemma misc Discrete-time system misc Time-varying systems misc Automation misc Discrete-time systems misc Performance analysis misc Symmetric matrices misc time-varying delay misc Linear matrix inequalities misc Delays |
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Summation Inequalities to Bounded Real Lemmas of Discrete-Time Systems With Time-Varying Delay |
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Summation Inequalities to Bounded Real Lemmas of Discrete-Time Systems With Time-Varying Delay |
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Zhang, Chuan-Ke |
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IEEE transactions on automatic control |
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summation inequalities to bounded real lemmas of discrete-time systems with time-varying delay |
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Summation Inequalities to Bounded Real Lemmas of Discrete-Time Systems With Time-Varying Delay |
| abstract |
Summation inequality is an important technique for analysis of discrete-time systems with a time-varying delay. It seems that from the literature a tighter inequality usually leads to a less conservative criterion. Based on <inline-formula><tex-math notation="LaTeX">H_{\infty}</tex-math></inline-formula> performance analysis problem, this note presents different findings on the relationship between the conservatism of bounded real lemma (BRL) and the tightness of summation inequality. Firstly, the BRL obtained by the Wirtinger-based inequality (WBI) is not always less conservative than the one by the Jensen-based inequality although the WBI is tighter. Secondly, the WBI is tighter than a general free-matrix-based inequality (GFMBI) developed in this note, while the BRL obtained via the GFMBI is less conservative than the WBI-based BRL. Finally, a numerical example is given to demonstrate those findings. |
| abstractGer |
Summation inequality is an important technique for analysis of discrete-time systems with a time-varying delay. It seems that from the literature a tighter inequality usually leads to a less conservative criterion. Based on <inline-formula><tex-math notation="LaTeX">H_{\infty}</tex-math></inline-formula> performance analysis problem, this note presents different findings on the relationship between the conservatism of bounded real lemma (BRL) and the tightness of summation inequality. Firstly, the BRL obtained by the Wirtinger-based inequality (WBI) is not always less conservative than the one by the Jensen-based inequality although the WBI is tighter. Secondly, the WBI is tighter than a general free-matrix-based inequality (GFMBI) developed in this note, while the BRL obtained via the GFMBI is less conservative than the WBI-based BRL. Finally, a numerical example is given to demonstrate those findings. |
| abstract_unstemmed |
Summation inequality is an important technique for analysis of discrete-time systems with a time-varying delay. It seems that from the literature a tighter inequality usually leads to a less conservative criterion. Based on <inline-formula><tex-math notation="LaTeX">H_{\infty}</tex-math></inline-formula> performance analysis problem, this note presents different findings on the relationship between the conservatism of bounded real lemma (BRL) and the tightness of summation inequality. Firstly, the BRL obtained by the Wirtinger-based inequality (WBI) is not always less conservative than the one by the Jensen-based inequality although the WBI is tighter. Secondly, the WBI is tighter than a general free-matrix-based inequality (GFMBI) developed in this note, while the BRL obtained via the GFMBI is less conservative than the WBI-based BRL. Finally, a numerical example is given to demonstrate those findings. |
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| title_short |
Summation Inequalities to Bounded Real Lemmas of Discrete-Time Systems With Time-Varying Delay |
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He, Yong Jiang, Lin Wu, Min Zeng, Hong-Bing |
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