Non-fragile Guaranteed Cost Controller Design for Discrete Descriptor Systems with Parameter Uncertainty

This paper is concerned with the design problem of non-fragile guaranteed cost controller for discrete descriptor systems with parameter uncertainty. The controller gain variations are assumed to be time-invariant and norm-bounded appearing in the controller coefficients. Sufficient conditions for the existence of a static state feedback guaranteed cost controller with additive uncertainty and multiplicative uncertainty are obtained in terms of a set of matrix inequalities, respectively. With these conditions, the problems of non-fragile guaranteed cost controller for discrete descriptor systems are solved. Explicit expressions of desired non-fragile state feedback guaranteed cost controllers are also given, and no matrix decomposition is required. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.