Delay-dependent robust H∞ control for discrete systems with time-delay and polytopic uncertainty

This paper describes a new separated structure for the analysis and synthesis of a class of discrete time-delay systems. For a wide range of problems such as robust analysis and synthesis for real polytopic uncertainty, multiobjective control and multichannel control problems, the separated structure between Lyapunov matrix and controller matrix leads to potentially less conservative results. This comes from the fact that it can rule out the technical restriction of using a single Lyapunov function to some extent. Then the robust H_∞ controller is designed for discrete systems with time-delay and polytopic uncertainty. All the conditions are delay-dependent and given in terms of LMIs. A numerical example is included to illustrate the effectiveness of the proposed representations.