Necessary and sufficient conditions for stability of impulsive switched linear systems

This paper addresses fundamental stability problems of impulsive switched linear systems, featuring given impulsive switching time intervals and switching rules. First, based on the state dynamical behaviors, we construct a new state transition-like matrix, called an impulsive-type state transition...

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Main Authors: Xu, H., Teo, Kok Lay, Gui, W.
Format: Journal Article
Published: AIMS 2011
Online Access:http://hdl.handle.net/20.500.11937/26874
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author Xu, H.
Teo, Kok Lay
Gui, W.
author_facet Xu, H.
Teo, Kok Lay
Gui, W.
author_sort Xu, H.
building Curtin Institutional Repository
collection Online Access
description This paper addresses fundamental stability problems of impulsive switched linear systems, featuring given impulsive switching time intervals and switching rules. First, based on the state dynamical behaviors, we construct a new state transition-like matrix, called an impulsive-type state transition (IST) matrix. Then, based on the IST matrix and Lyapunov stability theory, necessary and sufficient conditions for the uniform stability, uniform asymptotic stability, and exponential stability of impulsive switched linear systems are established. These stability conditions require the testing on the IST matrix of the impulsive switched linear systems. The results can be reduced to those for switched linear systems without impulsive effects, and also to those for impulsive linear systems without switchings.
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format Journal Article
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institution Curtin University Malaysia
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last_indexed 2025-11-14T08:03:24Z
publishDate 2011
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spelling curtin-20.500.11937-268742017-09-13T16:08:11Z Necessary and sufficient conditions for stability of impulsive switched linear systems Xu, H. Teo, Kok Lay Gui, W. This paper addresses fundamental stability problems of impulsive switched linear systems, featuring given impulsive switching time intervals and switching rules. First, based on the state dynamical behaviors, we construct a new state transition-like matrix, called an impulsive-type state transition (IST) matrix. Then, based on the IST matrix and Lyapunov stability theory, necessary and sufficient conditions for the uniform stability, uniform asymptotic stability, and exponential stability of impulsive switched linear systems are established. These stability conditions require the testing on the IST matrix of the impulsive switched linear systems. The results can be reduced to those for switched linear systems without impulsive effects, and also to those for impulsive linear systems without switchings. 2011 Journal Article http://hdl.handle.net/20.500.11937/26874 10.3934/dcdsb.2011.16.1185 AIMS unknown
spellingShingle Xu, H.
Teo, Kok Lay
Gui, W.
Necessary and sufficient conditions for stability of impulsive switched linear systems
title Necessary and sufficient conditions for stability of impulsive switched linear systems
title_full Necessary and sufficient conditions for stability of impulsive switched linear systems
title_fullStr Necessary and sufficient conditions for stability of impulsive switched linear systems
title_full_unstemmed Necessary and sufficient conditions for stability of impulsive switched linear systems
title_short Necessary and sufficient conditions for stability of impulsive switched linear systems
title_sort necessary and sufficient conditions for stability of impulsive switched linear systems
url http://hdl.handle.net/20.500.11937/26874