Robust H∞ guaranteed cost control of uncertain singular systems with mixed time-varying and nonlinear perturbation

This paper discusses the robust H_∞ guaranteed cost control problem for a class of uncertain singular systems with mixed time-varying and nonlinear perturbation. Guaranteed cost controller is derived by means of Lyapunov stability theory and linear matrix inequality approach. For all admissible uncertainties, the state feedback controller ensures that the closed-loop system not only possess a robust stability, but also meets the H_∞ performance. In this article, the guaranteed cost controller of the system is presented in the form of linear matrix inequality. Then, design problems of guaranteed controllers for uncertain singular systems are converted into convex optimization problems with linear matrix inequalities constraints. Finally, a numerical example is provided to demonstrate the results.