H2 and H∞ control of time-varying delay switched linear systems with application to sampled-data control

This paper deals with switched linear systems subject to time-varying delay. The main goal is to design state and output feedback switching strategies preserving closed-loop stability and a guaranteed H2 or H∞ performance. The switching strategies are based on a generalization of a recent extended version of the small gain theorem and do not require any assumption on the continuity of the delay and its time-variation rate. The key point to obtain the design conditions is the adoption of an equivalent switched linear system where the time-varying delay is modeled as a norm-bounded perturbation. Moreover, with this approach, it is possible to deal with sampled-data control systems. All conditions are formulated in terms of Lyapunov-Metzler inequalities, which allow the maximization of an upper bound on the time-delay preserving stability and guaranteed performance. Numerical examples are discussed in order to illustrate the effectiveness of the design approach.