Exponential stability and L2 control for delayed switched systems with mode-dependent average dwell time

Abstract

This paper investigates the problem of robustly globally uniformly exponential stability and L2 control for a class of switched systems with time-varying delay by using mode-dependent average dwell time (MDADT) approach. The MDADT approach is more applicable in practice than the average dwell time method in which each mode in the underlying system has its own average dwell time. Firstly, some sufficient conditions for robustly exponential stability is given by using the MDADT approach and piecewise Lyapunov function. Secondly, the L2-gain of the switched system with the external disturbance is analyzed. Then, the state feedback controller gain is obtained to ensure the exponential stability of the switched system. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.