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 time-delay 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.