Stabilization of Switched Systems on Non-Uniform Time Domain with Dwell Time

In this paper, we will present new stability conditions for a special class of linear switched systems, that evolves on non-uniform time domain. The considered systems switch between continuous-time subsystems on intervals with variable lengths, and discrete-time subsystems with variable step sizes. Time scales theory is introduced to derive conditions for exponential stability of this special class of switched systems by using the dwell time approach. The conditions are based on the existence of a multiple Lyapunov function. This shows that this class of switched systems can be stabilized if the dwell time of each continuous-time subsystem is greater than some bound, and if the gap of the discrete-time subsystem is bounded by some specific values. Numerical examples are presented to show the effectiveness of the proposed scheme.