Basics on stabilization of discrete switched systems

This paper is devoted to discuss the role of the minimum residence time in the stabilization of dynamic discrete switched systems. It is found that it can be obviated if the sampling period is sufficiently large even without imposing the requirement in the continuous-time case that the various switched parameterizations (referred to often as “ configurations”) possess a common Lyapunov function. However, it is claimed that the same role related to needing a sufficiently large minimum residence time at each stable parameterization in the continuous-time case is now played by the need of a sufficiently large minimum stabilizing sampling period. This requirement is removed if the various parameterizations possess a common Lyapunov function.