Robust Analysis And Control Synthesis For Uncertain Systems

In applied control systems, there exist various uncertainties in different degrees. For many applied control systems, the accurate mathematical models are hardly established. Therefore, it is difficult to apply widely modern control theory, which dependent on accurate mathematical models, to applied control systems. Luckily, the robustness lighten the applied road of morden control theory, and set up a bridge between modern control theory and applied control systems.In order to deal with uncertain phenomenon in applied control systems, such as parameter uncertainties, actuator failure, sensor failure, nonlinear perturbation, time-delay uncertainties, cost uncertainties, etc, the dissertation systematically studies the robust stability problems and the design methods of robust controller for three classes of control systems. These classes include linear uncertain systems, linear uncertain time-delay systems, and nonlinear uncertain time-delay systems. The dissertation is divided into four parts. Part one is about the subject of grading robust stabilization for linear uncertain systems. Part two studies the problems of reliable robust stabilization for linear uncertain time-delay system. Part three deals with the problems of robust stability and robust stabilization for nonlinear time-delay systems (discrete-time and continuous-time). Part four studied mainly the problems of time-dependent robust stability, and the design methods of delay-dependent robust controllers for nonlinear continuous time-delay systems.The main results in the dissertation are as follows.Evolution on control science is retrospected briefly, and the development of robust control theory related to the dissertation is introduced. The recent research problems with respect to uncertain systems (that include grading robust control, reliable robust control, guaranteed cost robust control, maximum of nonlinear perturbing bound, delay-dependent robust control) and our research works are reviewed in detail.General stability theory and Lyapunov stability theory of time-delay systems are introduced, which mainly include some definitions and results of time-independent stability and time-dependent stability. Based on the above theory, the robust stability dependent on delay-change-rate for time-delay systems with nonlinear perturbations is studied. Some criteria of the robust stability dependent on delay-change-rate is presented in an LMI framework, and an optimal algorithm about computing maximal bound of delay-change-rate is established while the system is robust stable.A new model of uncertain time-varying parameters for linear uncertain continuous systems is proposed. The problem of grading robust stabilization for such systems via state feedback is studied, and a sufficient criterion for the existence of such controller is presented in a LMI framework. Based on this LMI criterion, some foundational theory for the grading robust stabilization for such systems is established.A new model of measure sensor failure for linear uncertain continuous systems is proposed. The problems of grading robust stabilization and reliable grading robust stabilization for such systems via dynamic compensator are studied, and some conditions for the existence of such two classes of controllers are obtained in quasi linear matrix inequalities (Q-LMIS) forms. Using LMI approach, a linear convex optimization method, which improves the computing solvability of the Q-LMIS, is put forward.In the case of actuator failures (include partial degrade, normal case, complete outage case), the problems of reliable guaranteed robust stabilization and reliable guaranteed cost robust stabilization for linear uncertain time-delay systems, via state feedback containing actuator failures, are studied. The design methods for such controllers are proposed, and some LMI-based optimal algorithms for such controllers are presented.In the case of measure sensor failures (include partial degrade, normal case,complete outage case), the problem of reliable guaranteed robust stabilization for linear uncertain time-delay systems via dynamic compensator containing sensor failures is studied. A criterion of existence for such controller is obtained, and some design methods for such controller are presented.A new and more general model of nonlinear perturbations for discrete time-delay systems is proposed. The robust stability and the robust stability with Guaranteed cost for such systems are studied, and some LMI-based criteria of the robust stability and the robust stability with Guaranteed cost are presented. A linear convex optimization method with LMI constraints for computing maximal perturbation bound is presented, and an optimal procedure for decreasing the guaranteed cost is put forward.A new and more general model of nonlinear perturbations for continuous time-delay systems is presented, and the problems of robust control syntheses for time-delay systems with such nonlinear perturbations are studied. According to different cases, three classes of robust control problems are proposed. Firstly, the maximal problem of the time-delay change rate is put forward under the known extent of nonlinear perturbations, and a feasible criterion is given in a convex optimization form with LMI constraints. Secondly, the maximal bound problem of nonlinear perturbations is proposed for given extent of time-delay change rate, and a solving method based on the minimization procedure of weighting linear function with LMI constraints is established for such problem. Thirdly, a piecewise robust control problem for such systems is studied;an LMI-based design method of such controller is presented.The problems of delay-dependent robust stability and delay-dependent robust stability with guaranteed cost for time-delay systems with nonlinear perturbations, are studied. Some LMI-based criteria of delay-dependent robust stability and delay-dependent robust stability with guaranteed cost for such systems are established. Based on these criteria, a linear convex optimal method for decreasing the value of the guaranteed cost is given.The problem of delay-dependent robust stabilization for time-delay continuous systems with nonlinear perturbations is studied. Two classes of delay-dependent robust stable controllers: state feedback and delay-state feedback, are concerned. Some existent criteria and design methods of such two controllers are presented.