Delay-Dependent Robust H2 Control for Discrete Systems with Time-Delay and Polytopic Uncertainty

In this paper, new separated delay-dependent H2 performance criterion is derived for a class of discrete timedelay systems. When used in robust synthesis for real polytopic uncertainty, it can rule out the technical restriction of using a single Lyapunov function to some extent, and therefore, lead to potentially less conservative linear matrix inequality (LMI) characterizations. The results are then extended to design robust H2 controller for discrete systems with time-delay and polytopic uncertainty. All the conditions are given in terms of LMIs. A numerical example is given to illustrate the proposed method.