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