LMI approach to non-fragile guaranteed cost control of uncertain discrete time-delay systems

This paper studies the non-fragile Guaranteed Cost Control (GCC) problem via memoryless state-feedback controllers for a class of uncertain discrete time-delay linear systems. The systems are assumed to have norm-bounded, time-varying parameter uncertainties in the state, delay-state, input, delay-input and state-feedback gain matrices. Existence of the guaranteed cost controllers are related to solutions of some linear matrix inequalities (LMIs). The non-fragile GCC state-feedback controllers are designed based on a convex optimization problem with LMI constraints to minimize the guaranteed cost of the resultant closed-loop systems. Numerical examples are given to illustrate the design methods.