Quadratic stabilization control for a class of switched linear systems with state and input time-delays

A class of switched systems with Time-varying state and input delay is studied in this paper through connect the free-weighting matrix approach, Newton-Leibniz formula. By using the Lyapunov-Krasovskii functiong and multiple-Lyapunov function, a sufficient condition of the existence of controller with delay-dependent stability is given. Adjusting the corresponding parameters in the free-weighting matrix, a controller optimization algorithm is derived. As a special case, the results on delay-dependent/delay -derivative-independent stability and the existence of controller is obtained.