A dwell time approach for the stabilization of mixed Continuous/Discrete switched systems

In this paper, we study the stabilization properties of Continuous/Discrete switched systems using the dwell time approaches. The considered system switches between a continuous-time subsystem evolving on time intervals with variable lengths and a discrete-time subsystem with variable discrete step sizes. Since the time domain is non-uniform, and the stability of the discrete-time subsystem with variable discrete step sizes does not depend only on the dynamic of the system, but also on the length of the discrete steps, the usual conditions of dwell time approaches may not be applicable to stabilize this special class of switched systems. Motivated by that, stabilizing dwell time and average dwell time conditions are derived by introducing the time scales theory and numerical examples are proposed to illustrate the effectiveness of the proposed methods.