Robust H ∞ guaranteed cost control for uncertain switched descriptor delayed systems with nonlinear disturbance

Abstract

This article considers the issues of robust $H_{\infty }$ guaranteed cost control and memory state feedback stabilization for a class of uncertain switched descriptor delayed systems with nonlinear disturbance. Sufficient conditions for the existences of robust $H_{\infty }$ guaranteed cost controller in terms of linear matrix inequalities and switching strategy are proposed based on generalized Lyapunov function and convex optimization approach, and the memory state feedback controller ensures that the closed-loop systems satisfy the guaranteed cost function with a prescribed $H_{\infty }$ $\gamma$ -disturbance attenuation. Moreover, a convex optimization problem with linear matrix inequality constraints is formulated and solved by mean of the linear matrix inequality toolbox, and the optimal $H_{\infty }$ guaranteed cost memory state feedback controller with an upper bound of cost function is obtained. Finally, a numerical example illustrates the effectiveness of the proposed method.