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Zhai, Guisheng; Xu, Xuping; Ho, Daniel W. C.

Stability of switched linear discrete-time descriptor systems: a new commutation condition. (English) Zbl 1401.93161

Int. J. Control 85, No. 11, 1779-1788 (2012).
Summary: In this article, we study stability of switched linear discrete-time descriptor systems. Under the assumption that all subsystems are stable and there is no impulse occurring at the switching instants, we establish a new pairwise commutation condition under which the switched system is stable. It turns out that the condition is a natural and important extension to the existing commutation conditions, and it can be applied in discretised continuous-time switched systems in a straightforward manner. Finally, we also show that when the proposed commutation condition holds, there exists a common quadratic Lyapunov function for the subsystems.

Cited in 10 Documents

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C55 Discrete-time control/observation systems
93C05 Linear systems in control theory

Keywords:

switched linear discrete-time descriptor systems; stability; pairwise commutation; impulse-free switching; common quadratic Lyapunov functions; matrix inequalities
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References:

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