Non-fragile H-infinity controller design for discrete-time descriptor systems

This paper is concerned with the design problem of non-fragile H-infinity controller for discrete-time descriptor systems. 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 H-infinity controller with additive uncertainty and multiplicative uncertainty are obtained in terms of a set of matrix inequalities, respectively. With these conditions, the design problems of non-fragile H-infinity controller for discrete-time descriptor systems are solved. Explicit expressions of desired non-fragile state feedback H-infinity controllers are also given, and no matrix decomposition is required. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.