New conditions for stabilization and l2-gain analysis of discrete-time switched systems

Abstract

This paper uses a time-varying state feedback control method to investigate the global asymptotic stabilization issue of discrete-time switched systems with dwell-time constraints. A discrete dwell-time partitioning technique is proposed to design a time-varying Lyapunov function, which has a distinct characteristic that its value decreases at any time, even at each switching instant. Applying the partitioning technique and the time-varying control method, some new conditions with adjustable computational complexity are derived for stabilizing the discrete-time switched systems. Moreover, the extension to $l_2$-gain computation is presented in the sequel. Four examples are provided to illustrate the merits of the theoretical analysis.