A Relaxed Small-Gain Theorem for Interconnected Discrete-Time Systems

This technical note presents a relaxation of the small-gain theorem for the stability analysis of interconnected discrete-time nonlinear systems. The distinctive feature of this relaxation is that separate systems may be unstable, while global asymptotic stability (GAS) of the overall interconnected...
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Autor*in:	Geiselhart, Roman [verfasserIn] Lazar, Mircea Wirth, Fabian R

Format:	Artikel
Sprache:	Englisch

Erschienen:	2015

Rechteinformationen:	Nutzungsrecht: © Copyright (c) Geiselhart, R; Copyright (c) Lazar, M Mircea; Copyright (c) Wirth, FR

Schlagwörter:	distinctive feature Interconnected systems relaxed small gain theorem interconnected discrete-time nonlinear systems interconnected discrete-time systems stability analysis discrete time systems small-gain theorem GAS Lyapunov methods Vectors Discrete-time systems asymptotic stability Lyapunov function Nonlinear systems nonlinear control systems overall interconnected system global asymptotic stability

Übergeordnetes Werk:	Enthalten in: IEEE transactions on automatic control - New York, NY : Inst., 1963, 60(2015), 3, Seite 812-817
Übergeordnetes Werk:	volume:60 ; year:2015 ; number:3 ; pages:812-817

Links:	Volltext Link aufrufen Link aufrufen

DOI / URN:	10.1109/TAC.2014.2332691

Katalog-ID:	OLC1962551571

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540			\|a Nutzungsrecht: © Copyright (c) Geiselhart, R; Copyright (c) Lazar, M Mircea; Copyright (c) Wirth, FR
650		4	\|a distinctive feature
650		4	\|a Interconnected systems
650		4	\|a relaxed small gain theorem
650		4	\|a interconnected discrete-time nonlinear systems
650		4	\|a interconnected discrete-time systems
650		4	\|a stability analysis
650		4	\|a discrete time systems
650		4	\|a small-gain theorem
650		4	\|a GAS
650		4	\|a Lyapunov methods
650		4	\|a Vectors
650		4	\|a Discrete-time systems
650		4	\|a asymptotic stability
650		4	\|a Lyapunov function
650		4	\|a Nonlinear systems
650		4	\|a nonlinear control systems
650		4	\|a overall interconnected system
650		4	\|a global asymptotic stability
700	1		\|a Lazar, Mircea \|4 oth
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allfields	10.1109/TAC.2014.2332691 doi PQ20160617 (DE-627)OLC1962551571 (DE-599)GBVOLC1962551571 (PRQ)c1509-f34a4f427dd745b467f8a236947e0527d7714bc5631c5033e0df797abd3472b30 (KEY)0005057120150000060000300812relaxedsmallgaintheoremforinterconnecteddiscreteti DE-627 ger DE-627 rakwb eng 620 DNB Geiselhart, Roman verfasserin aut A Relaxed Small-Gain Theorem for Interconnected Discrete-Time Systems 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This technical note presents a relaxation of the small-gain theorem for the stability analysis of interconnected discrete-time nonlinear systems. The distinctive feature of this relaxation is that separate systems may be unstable, while global asymptotic stability (GAS) of the overall interconnected systems equilibrium is obtained. In addition, a Lyapunov function for the overall interconnected system is explicitly derived. Necessity of the hypothesis of the small-gain theorem is established for a rather general class of GAS nonlinear systems. An illustrative example demonstrates the non-conservatism of the developed small-gain theorem. Nutzungsrecht: © Copyright (c) Geiselhart, R; Copyright (c) Lazar, M Mircea; Copyright (c) Wirth, FR distinctive feature Interconnected systems relaxed small gain theorem interconnected discrete-time nonlinear systems interconnected discrete-time systems stability analysis discrete time systems small-gain theorem GAS Lyapunov methods Vectors Discrete-time systems asymptotic stability Lyapunov function Nonlinear systems nonlinear control systems overall interconnected system global asymptotic stability Lazar, Mircea oth Wirth, Fabian R oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 60(2015), 3, Seite 812-817 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:60 year:2015 number:3 pages:812-817 http://dx.doi.org/10.1109/TAC.2014.2332691 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6843917 http://repository.tue.nl/784941 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_30 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 60 2015 3 812-817
spelling	10.1109/TAC.2014.2332691 doi PQ20160617 (DE-627)OLC1962551571 (DE-599)GBVOLC1962551571 (PRQ)c1509-f34a4f427dd745b467f8a236947e0527d7714bc5631c5033e0df797abd3472b30 (KEY)0005057120150000060000300812relaxedsmallgaintheoremforinterconnecteddiscreteti DE-627 ger DE-627 rakwb eng 620 DNB Geiselhart, Roman verfasserin aut A Relaxed Small-Gain Theorem for Interconnected Discrete-Time Systems 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This technical note presents a relaxation of the small-gain theorem for the stability analysis of interconnected discrete-time nonlinear systems. The distinctive feature of this relaxation is that separate systems may be unstable, while global asymptotic stability (GAS) of the overall interconnected systems equilibrium is obtained. In addition, a Lyapunov function for the overall interconnected system is explicitly derived. Necessity of the hypothesis of the small-gain theorem is established for a rather general class of GAS nonlinear systems. An illustrative example demonstrates the non-conservatism of the developed small-gain theorem. Nutzungsrecht: © Copyright (c) Geiselhart, R; Copyright (c) Lazar, M Mircea; Copyright (c) Wirth, FR distinctive feature Interconnected systems relaxed small gain theorem interconnected discrete-time nonlinear systems interconnected discrete-time systems stability analysis discrete time systems small-gain theorem GAS Lyapunov methods Vectors Discrete-time systems asymptotic stability Lyapunov function Nonlinear systems nonlinear control systems overall interconnected system global asymptotic stability Lazar, Mircea oth Wirth, Fabian R oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 60(2015), 3, Seite 812-817 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:60 year:2015 number:3 pages:812-817 http://dx.doi.org/10.1109/TAC.2014.2332691 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6843917 http://repository.tue.nl/784941 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_30 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 60 2015 3 812-817
allfields_unstemmed	10.1109/TAC.2014.2332691 doi PQ20160617 (DE-627)OLC1962551571 (DE-599)GBVOLC1962551571 (PRQ)c1509-f34a4f427dd745b467f8a236947e0527d7714bc5631c5033e0df797abd3472b30 (KEY)0005057120150000060000300812relaxedsmallgaintheoremforinterconnecteddiscreteti DE-627 ger DE-627 rakwb eng 620 DNB Geiselhart, Roman verfasserin aut A Relaxed Small-Gain Theorem for Interconnected Discrete-Time Systems 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This technical note presents a relaxation of the small-gain theorem for the stability analysis of interconnected discrete-time nonlinear systems. The distinctive feature of this relaxation is that separate systems may be unstable, while global asymptotic stability (GAS) of the overall interconnected systems equilibrium is obtained. In addition, a Lyapunov function for the overall interconnected system is explicitly derived. Necessity of the hypothesis of the small-gain theorem is established for a rather general class of GAS nonlinear systems. An illustrative example demonstrates the non-conservatism of the developed small-gain theorem. Nutzungsrecht: © Copyright (c) Geiselhart, R; Copyright (c) Lazar, M Mircea; Copyright (c) Wirth, FR distinctive feature Interconnected systems relaxed small gain theorem interconnected discrete-time nonlinear systems interconnected discrete-time systems stability analysis discrete time systems small-gain theorem GAS Lyapunov methods Vectors Discrete-time systems asymptotic stability Lyapunov function Nonlinear systems nonlinear control systems overall interconnected system global asymptotic stability Lazar, Mircea oth Wirth, Fabian R oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 60(2015), 3, Seite 812-817 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:60 year:2015 number:3 pages:812-817 http://dx.doi.org/10.1109/TAC.2014.2332691 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6843917 http://repository.tue.nl/784941 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_30 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 60 2015 3 812-817
allfieldsGer	10.1109/TAC.2014.2332691 doi PQ20160617 (DE-627)OLC1962551571 (DE-599)GBVOLC1962551571 (PRQ)c1509-f34a4f427dd745b467f8a236947e0527d7714bc5631c5033e0df797abd3472b30 (KEY)0005057120150000060000300812relaxedsmallgaintheoremforinterconnecteddiscreteti DE-627 ger DE-627 rakwb eng 620 DNB Geiselhart, Roman verfasserin aut A Relaxed Small-Gain Theorem for Interconnected Discrete-Time Systems 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This technical note presents a relaxation of the small-gain theorem for the stability analysis of interconnected discrete-time nonlinear systems. The distinctive feature of this relaxation is that separate systems may be unstable, while global asymptotic stability (GAS) of the overall interconnected systems equilibrium is obtained. In addition, a Lyapunov function for the overall interconnected system is explicitly derived. Necessity of the hypothesis of the small-gain theorem is established for a rather general class of GAS nonlinear systems. An illustrative example demonstrates the non-conservatism of the developed small-gain theorem. Nutzungsrecht: © Copyright (c) Geiselhart, R; Copyright (c) Lazar, M Mircea; Copyright (c) Wirth, FR distinctive feature Interconnected systems relaxed small gain theorem interconnected discrete-time nonlinear systems interconnected discrete-time systems stability analysis discrete time systems small-gain theorem GAS Lyapunov methods Vectors Discrete-time systems asymptotic stability Lyapunov function Nonlinear systems nonlinear control systems overall interconnected system global asymptotic stability Lazar, Mircea oth Wirth, Fabian R oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 60(2015), 3, Seite 812-817 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:60 year:2015 number:3 pages:812-817 http://dx.doi.org/10.1109/TAC.2014.2332691 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6843917 http://repository.tue.nl/784941 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_30 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 60 2015 3 812-817
allfieldsSound	10.1109/TAC.2014.2332691 doi PQ20160617 (DE-627)OLC1962551571 (DE-599)GBVOLC1962551571 (PRQ)c1509-f34a4f427dd745b467f8a236947e0527d7714bc5631c5033e0df797abd3472b30 (KEY)0005057120150000060000300812relaxedsmallgaintheoremforinterconnecteddiscreteti DE-627 ger DE-627 rakwb eng 620 DNB Geiselhart, Roman verfasserin aut A Relaxed Small-Gain Theorem for Interconnected Discrete-Time Systems 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This technical note presents a relaxation of the small-gain theorem for the stability analysis of interconnected discrete-time nonlinear systems. The distinctive feature of this relaxation is that separate systems may be unstable, while global asymptotic stability (GAS) of the overall interconnected systems equilibrium is obtained. In addition, a Lyapunov function for the overall interconnected system is explicitly derived. Necessity of the hypothesis of the small-gain theorem is established for a rather general class of GAS nonlinear systems. An illustrative example demonstrates the non-conservatism of the developed small-gain theorem. Nutzungsrecht: © Copyright (c) Geiselhart, R; Copyright (c) Lazar, M Mircea; Copyright (c) Wirth, FR distinctive feature Interconnected systems relaxed small gain theorem interconnected discrete-time nonlinear systems interconnected discrete-time systems stability analysis discrete time systems small-gain theorem GAS Lyapunov methods Vectors Discrete-time systems asymptotic stability Lyapunov function Nonlinear systems nonlinear control systems overall interconnected system global asymptotic stability Lazar, Mircea oth Wirth, Fabian R oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 60(2015), 3, Seite 812-817 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:60 year:2015 number:3 pages:812-817 http://dx.doi.org/10.1109/TAC.2014.2332691 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6843917 http://repository.tue.nl/784941 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_30 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 60 2015 3 812-817
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source	Enthalten in IEEE transactions on automatic control 60(2015), 3, Seite 812-817 volume:60 year:2015 number:3 pages:812-817
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topic_facet	distinctive feature Interconnected systems relaxed small gain theorem interconnected discrete-time nonlinear systems interconnected discrete-time systems stability analysis discrete time systems small-gain theorem GAS Lyapunov methods Vectors Discrete-time systems asymptotic stability Lyapunov function Nonlinear systems nonlinear control systems overall interconnected system global asymptotic stability
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author	Geiselhart, Roman
spellingShingle	Geiselhart, Roman ddc 620 misc distinctive feature misc Interconnected systems misc relaxed small gain theorem misc interconnected discrete-time nonlinear systems misc interconnected discrete-time systems misc stability analysis misc discrete time systems misc small-gain theorem misc GAS misc Lyapunov methods misc Vectors misc Discrete-time systems misc asymptotic stability misc Lyapunov function misc Nonlinear systems misc nonlinear control systems misc overall interconnected system misc global asymptotic stability A Relaxed Small-Gain Theorem for Interconnected Discrete-Time Systems
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topic_title	620 DNB A Relaxed Small-Gain Theorem for Interconnected Discrete-Time Systems distinctive feature Interconnected systems relaxed small gain theorem interconnected discrete-time nonlinear systems interconnected discrete-time systems stability analysis discrete time systems small-gain theorem GAS Lyapunov methods Vectors Discrete-time systems asymptotic stability Lyapunov function Nonlinear systems nonlinear control systems overall interconnected system global asymptotic stability
topic	ddc 620 misc distinctive feature misc Interconnected systems misc relaxed small gain theorem misc interconnected discrete-time nonlinear systems misc interconnected discrete-time systems misc stability analysis misc discrete time systems misc small-gain theorem misc GAS misc Lyapunov methods misc Vectors misc Discrete-time systems misc asymptotic stability misc Lyapunov function misc Nonlinear systems misc nonlinear control systems misc overall interconnected system misc global asymptotic stability
topic_unstemmed	ddc 620 misc distinctive feature misc Interconnected systems misc relaxed small gain theorem misc interconnected discrete-time nonlinear systems misc interconnected discrete-time systems misc stability analysis misc discrete time systems misc small-gain theorem misc GAS misc Lyapunov methods misc Vectors misc Discrete-time systems misc asymptotic stability misc Lyapunov function misc Nonlinear systems misc nonlinear control systems misc overall interconnected system misc global asymptotic stability
topic_browse	ddc 620 misc distinctive feature misc Interconnected systems misc relaxed small gain theorem misc interconnected discrete-time nonlinear systems misc interconnected discrete-time systems misc stability analysis misc discrete time systems misc small-gain theorem misc GAS misc Lyapunov methods misc Vectors misc Discrete-time systems misc asymptotic stability misc Lyapunov function misc Nonlinear systems misc nonlinear control systems misc overall interconnected system misc global asymptotic stability
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title	A Relaxed Small-Gain Theorem for Interconnected Discrete-Time Systems
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title_full	A Relaxed Small-Gain Theorem for Interconnected Discrete-Time Systems
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doi_str_mv	10.1109/TAC.2014.2332691
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title_sort	relaxed small-gain theorem for interconnected discrete-time systems
title_auth	A Relaxed Small-Gain Theorem for Interconnected Discrete-Time Systems
abstract	This technical note presents a relaxation of the small-gain theorem for the stability analysis of interconnected discrete-time nonlinear systems. The distinctive feature of this relaxation is that separate systems may be unstable, while global asymptotic stability (GAS) of the overall interconnected systems equilibrium is obtained. In addition, a Lyapunov function for the overall interconnected system is explicitly derived. Necessity of the hypothesis of the small-gain theorem is established for a rather general class of GAS nonlinear systems. An illustrative example demonstrates the non-conservatism of the developed small-gain theorem.
abstractGer	This technical note presents a relaxation of the small-gain theorem for the stability analysis of interconnected discrete-time nonlinear systems. The distinctive feature of this relaxation is that separate systems may be unstable, while global asymptotic stability (GAS) of the overall interconnected systems equilibrium is obtained. In addition, a Lyapunov function for the overall interconnected system is explicitly derived. Necessity of the hypothesis of the small-gain theorem is established for a rather general class of GAS nonlinear systems. An illustrative example demonstrates the non-conservatism of the developed small-gain theorem.
abstract_unstemmed	This technical note presents a relaxation of the small-gain theorem for the stability analysis of interconnected discrete-time nonlinear systems. The distinctive feature of this relaxation is that separate systems may be unstable, while global asymptotic stability (GAS) of the overall interconnected systems equilibrium is obtained. In addition, a Lyapunov function for the overall interconnected system is explicitly derived. Necessity of the hypothesis of the small-gain theorem is established for a rather general class of GAS nonlinear systems. An illustrative example demonstrates the non-conservatism of the developed small-gain theorem.
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title_short	A Relaxed Small-Gain Theorem for Interconnected Discrete-Time Systems
url	http://dx.doi.org/10.1109/TAC.2014.2332691 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6843917 http://repository.tue.nl/784941
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up_date	2024-07-04T03:49:36.270Z
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