Robust H∞ Optimal Guaranteed Cost control for a Class of Nonlinear Uncertain Singular Systems with Delayed State

This paper concerns the problem of robust control for a class of nonlinear singular systems with state delayed and parameter uncertainties. The parameter uncertainty in the systems is norm-bounded and time-varying. The nonlinear terms are constrained in the finite Hurwitz sector. At first, the definition of robust Hαoptimal guaranteed cost systems with γdisturbance attenuation performance is presented. Then the design approach of a state feedback controller for optimizing the guaranteed cost is proposed. Based on an LMI approach, a sufficient condition for the existence of such controllers is given. The closed-loop system designed not only keeps stability for all admissible uncertainties, but also satisfies a specified gamma disturbance attenuation Hαperformance and provides a guaranteed cost.