Robust H∞ Control for Discrete Singular Systems with State Delay and Parameter Uncertainty

Abstract

This paper addresses the problems of robust stabilization and robust H∞ control for uncertain discrete singular systems with state delay and parameter uncertainties. The discrete singular delay system under consideration is not necessarily regular. The parameter uncertainties are assumed to be time invariant but norm-bounded. The purpose of the robust stabilization problem is the design of state feedback controllers such that, for all admissible uncertainties, the closed-loop system is regular, causal and stable, while for the robust H∞ control problem, in addition to the above requirements, a prescribed H∞ norm bound constraint is required to be enforced. In terms of non-strict LMIs, sufficient conditions for the solvability of the above problems are presented, and expressions of the desired state feedback controllers are also given. A numerical example is given to demonstrate the application of the proposed method.