This paper addresses the stability problem for a switched system formed by a finite family of linear subsystems
The authors assume that for each , there exists a stabilizing linear feedback for the th subsystem, and that the resulting family of closed-loop subsystems admits a common quadratic Lyapunov function.
The control law for the switched system is defined by means of a sequence of switching times . On each interval the control law may be indifferently defined as either (where is the active index for the th interval) or the sampled value .
The authors prove that asymptotic stability is guaranteed provided that the mesh size is sufficiently small.
The paper contains also a sufficient condition for the existence of a common Lyapunov function, and extensions of the result to systems with static output feedback and/or centralized/decentralized control.