Guaranteed Cost Control For Singular Systems With Parameter Uncertainty

It is inadequate that the general system guarantees its stability, so the dynamic response of general system satisfies the demand of some function index. Therefore, the question of guaranteed cost control for systems is put forward. In this paper, by using Lyapunov stability theory and the theory of LMI, we studied the problems of guaranteed cost control for three kinds of singular systems with parameter uncertainty, namely, the guaranteed cost control for linear singular systems with parameter uncertainty, the guaranteed cost control for singular systems with nonlinear perturbation, and the guaranteed cost control for periodically time-varying singular systems with parameter uncertainty.The main contents of this paper are as follows:Firstly, the present situation and the existent problems of guaranteed cost control are introduced. Secondly, the fundamental knowledge and prepared lemmas are considered. Finally, the main research task is studied in Chapter 3,4,5:(1) This part gives the sufficient condition of corresponding control law based on Lyapunov stability theory and the linear matrix inequality. Then, the numerical example shows the validity of our conclusion via the LMI-box.(2) In this part, we give the conclusions based on the guaranteed cost control of normal system with nonlinear perturbation. The controller itself will be fixed in a disturbance within the framework allowed by a group of matrix inequality equations, through the processing parameters matrix inequality methods, given the method of guaranteed cost controller of nonlinear singular systems. (3) The existent conditions of guaranteed control law of this part are based on the stability and admissibility for periodically time-varying singular systems. And this approach is applied in general periodically time-varying singular systems.