Robust Control And Filtering Of Switched Dynamic Systems

Switched systems are an important class of dynamical systems which are composed ofseveral continuous-time or discrete-time subsystems and a rule that orchestrates the switchingamong them. Many real world processes and systems can be modeled as switched systems.Considering the wide applications in practical projects, over the past decades, switched systemshave received more and more attentions, and their analysis and synthesis have been extensivelystudied. In this paper, the problems of exponential l2l?state feedback control, exponentiall2l?output tracking control, exponential l2l?robust filter, finite-time control, observer-based finite-time robust exponential l2l?control are considered, and some useful conclusionsare obtained. The main research work of this dissertation is listed as follows:1. The robust exponential l2l?control problem is considered for discrete-time switchedsystems with both time-varying delay and norm-bounded parameter uncertainties. An exponen-tial l2l?performance index is first introduced for the discrete-time switched systems, and theeffect of disturbance on the system is studied combined with this performance. The designedcontroller is a memory exponential l2l?controller. It is proved that the obtained result hasless conservativeness than the one developed via a memoryless controller. The disturbance re-jection capability of exponential l2l?performance index is researched, and the simulationshows that this performance has a better disturbance attenuation than the traditional l2l?performance.2. The problem of exponential l2l?output tracking control is considered for discrete-time switched systems with time-varying delay. The exponential l2l?performance index isfirst introduced to study this problem for discrete-time switched systems. The tracking signalis produced by a reference model. A new finite sum inequality lemma is given to deal with theforward difference of Lyapunov-Krasovskii functional. By resorting to the average dwell timeapproach, the switched signal is designed, and some new delay-dependent criteria guaranteeingexponential stability are developed. In addition, the corresponding solvability conditions us-ing cone complement linearization method for the desired exponential l2l?output trackingcontroller is established.3. The robust exponential l2l?filtering problem is addressed for discrete-time switched systems with polytopic uncertainties, which is solved via an average dwell time approach andLyapunov stability theory. The designed filter is related to both switched signal and polytopicuncertainties. Sufficient conditions in terms of strict linear matrix inequality (LMI) are derivedfor checking the robust exponential stability of a filtering error system. An explicit expressionfor the desired robust exponential filter is also given by Matlab tool box.4. The problems of finite-time state feedback control and observer-based finite-time robustexponential l2l?control are considered for discrete-time switched systems with time delay,respectively. First, the problem of finite-time state feedback control of discrete-time switchedsystems with time delay is studied. Then, to reduce the effect of disturbances on the system,the problem of observer-based finite-time robust exponential l2l?control is considered fora class of discrete-time switched systems with time delay and uncertainties. By resorting to theaverage dwell time approach and Lyapunov-Krasovskii functional technology, some new delay-dependent criteria guaranteeing finite-time boundedness and finite-time stability are developed.The state feedback controller and observer-based finite-time exponential l2l?controller arealso obtained by virtue of a cone complement linearization method.5. The problem of finite-time control is addressed for a class of continuous-time switcheddelay systems via dynamic output feedback. By resorting to the average dwell time approachand Lyapunov-Krasovskii functional technique, some new delay-dependent criteria guarantee-ing finite-time boundedness and finite-time stability are developed, respectively. An explicitexpression for the desired dynamic output feedback controller is also given by eliminating thecoupling between system matrix and Lyapunov matrix using a serious of inequalities.