Stability analysis of switched linear stochastic systems

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6 Citations (Scopus)

Abstract

In this paper, the stability analysis problem is considered for switched linear stochastic systems, where both stable and unstable subsystems are involved, by using the Lyapunov-like function approach. When there is a common Lyapunov-like function for all subsystems, it is shown that the switched system is globally asymptotically stable in probability (GAS-P) if the total activation time ratio of unstable subsystems to stable ones is less than a specified constant. When there is not a common Lyapunov-like function for all subsystems, the proposal is made to use the multiple Lyapunov-like function and to show that in addition to the total activation time ratio requirement, if the average dwell time is sufficiently large, then the switched stochastic system is GAS-P.

Original languageEnglish
Pages (from-to)661-669
Number of pages9
JournalProceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering
Volume222
Issue number7
DOIs
Publication statusPublished - 2008

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Stochastic systems
Chemical activation

Keywords

  • Average dwell time
  • Common Lyapunov-like function
  • Globally asymptotically stable in probability (GAS-P)
  • Multiple Lyapunov-like function
  • Stability analysis
  • Switched linear stochastic system

ASJC Scopus subject areas

  • Mechanical Engineering
  • Control and Systems Engineering

Cite this

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abstract = "In this paper, the stability analysis problem is considered for switched linear stochastic systems, where both stable and unstable subsystems are involved, by using the Lyapunov-like function approach. When there is a common Lyapunov-like function for all subsystems, it is shown that the switched system is globally asymptotically stable in probability (GAS-P) if the total activation time ratio of unstable subsystems to stable ones is less than a specified constant. When there is not a common Lyapunov-like function for all subsystems, the proposal is made to use the multiple Lyapunov-like function and to show that in addition to the total activation time ratio requirement, if the average dwell time is sufficiently large, then the switched stochastic system is GAS-P.",
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T1 - Stability analysis of switched linear stochastic systems

AU - Zhai, Guisheng

AU - Chen, Xinkai

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AB - In this paper, the stability analysis problem is considered for switched linear stochastic systems, where both stable and unstable subsystems are involved, by using the Lyapunov-like function approach. When there is a common Lyapunov-like function for all subsystems, it is shown that the switched system is globally asymptotically stable in probability (GAS-P) if the total activation time ratio of unstable subsystems to stable ones is less than a specified constant. When there is not a common Lyapunov-like function for all subsystems, the proposal is made to use the multiple Lyapunov-like function and to show that in addition to the total activation time ratio requirement, if the average dwell time is sufficiently large, then the switched stochastic system is GAS-P.

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KW - Common Lyapunov-like function

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