FEEDBACK CONTROL DESIGN FOR SWITCHED SYSTEMS WITH TIME-VARYING DELAY

Feedback control design is considered for stabilizing a discrete-time switched system with time-varying delay and time-varying uncertainty. In particular, we establish a practical method to construct feedback controllers to stabilize the system without requiring knowledge of the time-varying delay. First, we design feedback controllers which stabilize a non delayed switched system with time-varying uncertainty for any switching rule. Then, we quantify the maximum size of the time-varying delay which guarantees stability of the system of interest regardless of time-varying uncertainty. We achieve this via multiple Lyapunov functionals and the linear matrix inequalities framework.