TY - JOUR

T1 - Stability analysis of switched linear stochastic systems

AU - Zhai, G.

AU - Chen, X.

PY - 2008

Y1 - 2008

N2 - 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.

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.

KW - Average dwell time

KW - Common Lyapunov-like function

KW - Globally asymptotically stable in probability (GAS-P)

KW - Multiple Lyapunov-like function

KW - Stability analysis

KW - Switched linear stochastic system

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U2 - 10.1243/09596518JSCE569

DO - 10.1243/09596518JSCE569

M3 - Article

AN - SCOPUS:54549119120

VL - 222

SP - 661

EP - 669

JO - Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering

JF - Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering

SN - 0959-6518

IS - 7

ER -