Robust H∞ Disturbance Attenuation for Uncertain Discrete-Time Systems with Time-Varying Delay

This paper discusses robust H∞ disturbance attenuation of uncertain discrete-time systems that have time-varying delay in state. There have been only a few results on H∞ disturbance attenuation for discrete-time delay systems. Especially, few results on robust H∞ disturbance attenuation for a class of uncertain discrete-time delay systems have appeared in the literature. Therefore, the study of robust H∞ disturbance attenuation for uncertain discrete-time delay systems is a very important problem. We first obtain an H∞ disturbance attenuation condition for nominal discrete-time systems with time varying delay via linear matrix inequalities (LMIs). To this end, we define a new Lyapunov function and use Leibniz-Newton formula and free weighting matrix method, which reduce the conservativeness and unnecessary LMI slack variables in our robust H∞ disturbance attenuation conditions. Then we extend to a robust H∞ disturbance attenuation condition for uncertain discrete-time delay systems. Finally, we give some numerical examples to show that our conditions are less conservative than other results in the literature. Mathematics Subject Classification: 93E20