Robust Guaranteed Cost Control Of The Continuous Systems With Uncertain Parameters

In this paper, the guaranteed cost control problem of the uncertain continu- ous linear systems is studied by Lyapunov stability theory. The robust stability is analyzed and the sufficient conditions for the existence and the method of design for the robust guaranteed cost controller are given. The results that regarding the guaranteed cost control of continuous linear systems with uncertain parameters are extended to the more general uncertain systems.1. The robust guaranteed cost control for the uncertain continuous linear systemsThe problem of the robust guaranteed cost control for the continuous linear systems with uncertain parameters and nonlinear perturbation is studied. It is assumed that the uncertain parameters are of norm bounded uncertainty, matrix polytope structured uncertainty and highly structured uncertainty, and the nonlinear perturbation is the general nonlinear function of the state, which satisfies norm bound. The corresponding robust guaranteed cost controller with memoryless state feedback is given for three kinds of structured uncertainty respectively, which can make not only the systems robust stability but a given quadratic cost function satisfy a certain cost, and the design of controller is based on the feasible solutions of linear matrix inequality(LMI), then the corresponding examples are given to illustrate the case.2. The robust guaranteed cost control for the uncertain time-delay contin- uous linear systems The problem of the robust guaranteed cost control for the time-delay cont- inuous linear systems with the uncertain parameters and the nonlinear perturbation is studied. For the model with above three kinds of uncertainty and nonlinear perturbation, the nonlinear perturbation is the general nonlinear function of the state and the time-delay state. The corresponding sufficient conditions for the existence of the robust guaranteed cost controllers is obtained , and the design method of the robust guaranteed cost controllers with memory state feedback are given, where the controller parameters can be given by the feasible solution of LMIs, by using Lyapunov stability theory and combining appropriate matrix inequality technique. Finally, the relevant examples are constructed for the results obtained. Moreover the availability and the feasibility of the robust guaranteed cost controller design method are verified.