Discretized quasi‐time‐dependent control for continuous‐time switched linear systems with persistent dwell‐time

Abstract

Abstract This article is concerned with the dynamic output‐feedback control problem for continuous‐time switched linear systems with persistent dwell‐time (PDT). Considering the quasi‐periodic property of PDT switching, a discretized quasi‐time‐dependent (QTD) control scheme is proposed by means of a multiple discretized QTD Lyapunov function approach. This control scheme is devoted to designing discretized controllers for continuous‐time switched systems straightforwardly. Firstly, the stability and ‐gain of switched systems with PDT is analyzed utilizing multiple QTD Lyapunov functions. Then, by constructing the quadratic discretized version of these functions, a synthesis condition for the discretized QTD controller is established. In order to formulate the synthesis condition in terms of LMIs, we employ the controller state reset strategy in the derivation, which means that the controller state is reset to that of the plant at each switching instant. Finally, a numerical example is given to illustrate the effectiveness of the proposed control scheme.