Robust Guaranteed Cost Control For Uncertain Singular Systems

When practical problems in engineering with a pathological value of properties is studied for analysis and modeling, singular systems theory is an effective tool. Singular system, which is also known as the description of systems, differential-algebraic systems, generalized state space systems or semi-state systems, has a wider application background, and needs more perfect theoretical support. Research of robust control problems of singular systems has been extensive attention of experts and scholars, and some very systematic results are gained. In this paper, guaranteed cost control problem for both parameter uncertainty and nonlinear singular perturbation systems is in-depth studied and some meaningful results are obtained. The specific contents are included as follows:First, robust guaranteed cost control problem with the parameter uncertainty and nonlinear perturbation is studied for the singular systems. Fist of all, by using Lyapunov stability theory, for uncertain parameters of the system with the strong structural uncertainty, with matrix polytopic uncertainty and convex polyhedron uncertainty and certain assumptions that nonlinear perturbations satisfy, the conditions of robust guaranteed cost control for the system are given respectively, and the corresponding robust state-feedback guaranteed cost controller is designed, and the control gain matrix can be constructed by the solution of linear matrix inequalities to enhance the control of achievement.Second, robust guaranteed cost control problem with the parameter uncertainty and nonlinear perturbation of the time-delay singular systems is researched in the paper. For uncertain parameters of the system which meet the strong structural uncertainty, matrix polytopic uncertainty and convex polyhedron uncertainty and certain assumptions that nonlinear perturbations satisfy, by choosing appropriate Lyapunov-Krasovskii functional, and using of Lyapunov stability theory, the conditions of robust guaranteed cost control for the system are given respectively, and the corresponding robust state-feedback guaranteed cost controller is also designed. In the course of the research, By using of matrix operations and matrix inequality technique, the control gain matrix can also be transformed into the expression of solution of linear matrix inequalities, so that the achievement of the controller will be more convenient.Finall, in this paper, some numerical examples and computer simulation are presented to verify the conclusions, which also prove the validity of theoretical results obtained.