Guaranteed Cost Control Of Uncertain Delayed Singular Systems With Nonlinear Perturbation

In this thesis, we investigate guaranteed cost control problem for delayed singular systems with nonlinear perturbation. To begin with, general introduction of robust control, H∞control and guaranteed cost control for uncertain time-delay systems is given. Then, according to different needs of the controllers, we study guaranteed cost control problem. We show LMIs criteria for stability of closed-loop system, and present the guaranteed cost controller design method of the closed-loop system. The main content is summarized as follows:(1) We investigate H∞guaranteed cost control problem for time-delay singular systems with nonlinear structured perturbation. The perturbation is a function of state and state delay, and satisfies Lipschitz condition. A sufficient condition is given to guarantee robust stability and the performance index of closed-loop system satisfies certain supreme boundary. H∞memoryless controller is obtained by solving LMIs. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.(2) Guaranteed cost control problem for time-delay singular systems with nonlinear structured perturbation is discussed. The state matrix, state delay matrix and input matrix of the systems are supposed to have linear fractional uncertainties, and the nonlinear perturbation satisfies Lipschitz condition. In the thesis, the definition of generalized quadratically stable is introduced. Then we present sufficient condition to guarantee robust stability of the closed-loop system and the performance index of closed-loop system with certain supreme boundary. Furthermore, we give the state feedback controller design method. Finally, a numerical example is give to illustrate the validity of proposed method.(3) Non-fragile H∞guaranteed cost control problem for a class of multiple time-delay singular systems is investigated. We present a sufficient condition in terms of LMIs for the non-fragile H∞controller existed. The results obtained can ensure that the closed-loop system is stable and the performance index satisfies certain supreme boundary. Then, the controller with additive perturbation is presented. Finally, an example is given to demonstrate the effectiveness of the approach proposed.