Delay-Dependent Robust ℋ_∞ Output Feedback Control for Uncertain Discrete-Time Switched Systems with Interval Time-Varying Delay

This paper revisits the problem of delay-dependent dynamic output feedback control for a class of uncertain discrete-time switched linear state-delayed systems, where the state delay is assumed to be time-varying and of an interval-like type, which means that both the lower and upper bounds of the time-varying delay are available and the parameter uncertainties are assumed to have a structured linear fractional form. The objective is to design a switched dynamic output feedback controller guaranteeing the asymptotic stability of the resulting closed-loop system with disturbance attenuation level γ. Based on a new delay-dependent switched Lyapunov-Krasovskii functional combined with Finsler's Lemma, a novel sufficient condition for robust ℋ_∞ performance analysis is first derived and then the corresponding controller synthesis is developed. It is shown that the controller parameters can be obtained by solving a set of linear matrix inequalities, which are numerically efficient with commercially available software. Finally, a numerical example is provided to illustrate the advantages and less conservatism of the proposed approach in comparison with the existing approaches.