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Zbl 1119.34042
Zhai, Guisheng; Xu, Xuping; Lin, Hai; Michel, Anthony N.
Analysis and design of switched normal systems. (English)
[J] Nonlinear Anal., Theory Methods Appl. 65, No. 12, A, 2248-2259 (2006). ISSN 0362-546X

The stability for a class of switched systems composed of both continuous-time and discrete-time LTI normal subsystems are studied. The authors show that when all continuous-time systems are Hurwitz stable and all discrete-time subsystems are Schur stable, a common quadratic Lyapunov function $V(x)=x^Tx$ exists for the subsystems and thus the switched system is exponentially stable under arbitrary switching. They also show that when unstable subsystems are involved, if the activation time ratio between unstable subsystems and stable ones is less than a specified value, then the switched system is exponentially stable with the desired decay rate.
[Anh Cung (Hanoi)]

MSC 2000:: *34D20 Lyapunov stability of ODE
34A36 Discontinuous equations

Keywords: stability; common Lyapunov function; arbitrary switching; activation time ratio between stable and unstable subsystems

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