Design Of Robust Controller For Switched Systems With Uncertainty And Time Delay

Switched systems are a class of important hybrid systems which are composed of severalcontinuous-time or discrete-time subsystems and a rule that orchestrates the switching amongthem. Many real world processes and systems can be modeled as switched systems. Due tothe existence of the switching rule, their dynamics may become very complicated. Theinvolvement of the switching mechanism brings new insights as well as new challenges insystems&control and related fields. Meanwhile, research results of switched systems alsomake significant reference to general hybrid systems in terms of ideas, methods and theories.On the other hand, uncertainties and time-delays are frequently encountered in many practicalengineering systems, and are often the sources of instability and performance deterioration.Due to the interaction among them and switching rules, the behaviors of such systems arevery complex. Therefore, the study of switched systems deserves investigation for theoreticaldevelopment as well as for practical applications. This dissertation studies robust guaranteedcost control and robust H-infinity control problems for switched systems with uncertainty andtime delay. Lyapunov function method, convex combination technique and linear matrixinequalities method are three major methods adopted in the study. The main contributions areas follows.(1) The problem of robust H-infinity control for a class of switched singular systemswith time delay is discussed. By using Lyapunov function and linear matrix inequalityapproach, first of all, robust stability of a class of switched singular systems with time delay isproposed. Then, based on H-infinity control theory, a sufficient condition of H-infinitystability is presented in terms of matrix inequality. Next, sufficient condition of H-infinitycontrol is given under state feedback and output feedback. Finally, a numerical exampleillustrates the effectiveness of the method.(2) It is investigated that state feedback robust H-infinity control problem for a class ofuncertain switched systems with time delay. First of all, based on linear matrix inequalitymethod and convex combination technique, a sufficient condition for the existence of a class of uncertain time-delay switched singular systems’ robust H-infinity subcontrollers ispresented, which is in the form of matrix inequalities. The matrix inequalities are changedinto linear matrix inequalities by using variable substitution method. A simulation example isgiven to solve the gain matrices of state feedback robust H-infinity controllers. Then, thedesign of H-infinity robust controller and analysis of H-infinity robustness are given.(3) The problem of robust guaranteed cost control for a class of uncertain switchedsystems is studied. Suppose that the time-varying uncertain parameters of switched singularsystems are norm-bounded, but the matched conditions are not required to satisfy. A newsufficient condition of the existence of robust guaranteed cost controllers is given for systemsby constructing the generalized Lyaponov function and taking convex combination technique.Furthermore, a convex optimization problem with linear matrix inequalities constraints isformulated. Robust guaranteed cost control law and the minimization of the upper boundaryof closed-loop performance index are obtained. At the same time, the design problem ofoptimal guaranteed cost controller for a class of discrete-time switched systems is investigated.Finally, a numerical example is given to show the potential of the proposed technique.(4) The problem of robust guaranteed cost controller design for a class of uncertainswitched systems with time delay is investigated. A new sufficient condition of the existenceof guaranteed cost state feedback controllers is derived for the switched singular systems withboth state and input delays by taking the linear matrix inequality approach and robustguaranteed cost control theory. Furthermore, the robust guaranteed cost control for a class ofcontinuous-time uncertain time-delay switched singular systems and discrete-time uncertainswitched systems with time delay is considered. The problem of the robust guaranteed costcontroller design can be turned into the solvable problem of a set of linear matrix inequalities.Finally, a numerical example is given to show the potential of the proposed technique.