Minimax controller design for linear switched time-delay systems

In this paper, we investigate the disturbance attenuation of linear switched systems with constant time delay and disturbances by using Minimax. Based on the method of common Lyapunov function, we get a sufficient condition that guarantee asymptotic stability of the system with state feedback for the arbitrary switching signal. To overcome the limitation of the common Lyapunov function, we design appropriate switching rule and state feedback controller, using the combination of convex combination and Lyapunov function method, which can ensure the switched system to be asymptotically stable. In these two processes, we design a method to attenuate disturbances using Minimax, whose function is to get lower sensitivity to disturbances and strengthen the robustness. Two examples illustrate the effectiveness of proposed methods.