State feedback ℌ ∞ control of time-delay switched linear systems: A descriptor approach

In this paper we propose contributions on the control of switched linear systems subject to time-delays. Our methods allow to synthesize state feedback switching laws able to ensure the stabilization and the fulfillment of a prescribed ℌ ∞ disturbance attenuation property. The proposed criteria are delay-dependent and based on an application of the descriptor approach, previously introduced in the literature to study standard time-delay systems. The core of our procedure is based on the solution of sets of matrix inequalities, which allow simultaneously to assign a suitable switching law and to determine a feasible piecewise quadratic Lyapunov-Krasovskii functional associated to it.