Robust stabilization of switched systems with time-delay

This note deals with robust stabilization of switched systems with time-delay under arbitrarily switching sequences in the discrete-time domain. The proposed approach in this note detects the existence of a switched quadratic Lyapunov function to check asymptotic stability of the switched systems with time-delay tinder arbitrarily switching sequences. Two equivalent conditions based on linear matrix inequalities are developed for guaranteeing the stability of switched systems with time-delay under arbitrarily switching sequences. According to these conditions, the state feedback control law is given to ensure robust stabilization of switched systems with uncertainties. At last, a numerical example illustrates the reduction of conversation.