Stability and stabilization of discrete time switched systems

Abstract

This paper addresses two strategies for stabilization of discrete time linear switched systems. The first one is of open loop nature (trajectory independent) and is based on the determination of an upper bound of the minimum dwell time by means of a family of quadratic Lyapunov functions. The relevant point on dwell time calculation is that the proposed stability condition does not require the Lyapunov function be uniformly decreasing at every switching time. The second one is of closed loop nature (trajectory dependent) and is designed from the solution of what we call Lyapunov–Metzler inequalities from which the stability condition is expressed. Being non-convex, a more conservative but simpler to solve version of the Lyapunov–Metzler inequalities is provided. The theoretical results are illustrated by means of examples.