Study On Dissipativity And Some Design Problems Of Switched Discrete-Time Systems

As an important and special class of hybrid systems, switched systems are of great significance both in theory development and engineering applications. Switched systems have attracted increasing attention. A rapid progress has been made so far, most of the results on switched systems focus on stability. However, due to the complexity arising from interaction between the continuous dynamics and discrete dynamics, coupled with the co-design of controllers of subsystems and switching signals, the dynamic behavior of switched systems become very complicated and this makes the design of switched systems very difficult. Thus a lot of problems deserve investigation. On the other hand, dissipativity including passivity, as an important system property, has been widely applied in the analysis and design of non-switched systems and a systematical theory has been established. For switched systems, especially for switched discrete-time systems, the study on dissipativity is just at the early stage. Many problems are far from being understood and thus deserve investigation.This dissertation studies the dissipativity property, especially the passivity property and a few synthesis issues including output tracking, output regulation, and reliable control for several classes of switched discrete-time systems by using multiple Lyapunov functions. The main contributions are as follows.1. The problem of passivity and feedback passification for switched discrete-time linear systems is investigated and decomposable dissipativity for nonlinear systems is studied. For linear systems, conditions for feedback passivity of the system are obtained without the requirement of strict passivity of subsystems by using multiple Lyapunov functions. We then design switching laws and controllers of individual subsystems. First, when the complete state measurements are available, we design state feedback controllers for subsystems and a state-dependent switching law such that the closed-loop switched system is strict passive. Second, when only partial state measurements are available, dynamic output feedback controllers for subsystems are designed and a switching law depending only on the state of the output feedback controllers is constructed to guarantee strict passivity of the closed-loop switched system. For switched nonlinear systems, sufficient conditions guaranteeing decomposable dissipativity is derived under some switching law via multiple storage functions and multiple supply rates.2. Incremental passivity and the incremental passivity-based output regulation problem of switched discrete-time linear systems are investigated. First, the concept of incremental passivity for switched systems is given using multiple storage functions. Furthermore, conditions for a switched system to be incrementally passive are obtained without assuming the incremental passivity conditions for subsystems. Second, a switched internal model with incremental passivity is constructed, which closely links the solvability of the output regulation problem. A characteristic of the switched internal model is that it does not necessarily switch synchronously with the controlled plant, which greatly increases the freedom of design. Finally, it is shown that once the incremental passivity of the feedback interconnection between the controlled plant and the switched internal model is assured, the output regulation problem for switched systems is solvable via the designed controllers, even though the problem for none of subsystems is solvable.3. The H? output tracking control problem for switched discrete-time linear systems is considered without the requirement of the solvability conditions for subsystems. When the system states are available and the system matrix of the reference model is Hurwitz, the first part gives the sufficient conditions which guarantee the solvability of the tracking problem for the switched systems via multiple Lyapunov functions method. State feedback tracking controllers and a state-dependent switching law are designed such that the Hx model reference tracking performance is guaranteed. The second part focuses on the case that the system states are not available and the system matrix of the reference model is not required to be Hurwitz. By using weak multiple Lyapunov functions, sufficient conditions are obtained such that the tracking problem for the switched system is solvable, and output feedback controllers and an output error-dependent switching law are designed to satisfy the H? model reference tracking performance. In addition, the quadratic function corresponding to each subsystem is not required to be positive definite.4. The problem of output regulation for a class of switched discrete-time linear systems is addressed. When the problem for each subsystem may not be solvable and only the output tracking error is available, sufficient conditions for the problem to be solvable are given via design of an output error-dependent switching law and applying dynamical error feedback by using the weak multiple Lyapunov function. Furthermore, based on the solvability conditions, the controllers and switching law are designed. In addition, different coordinate transformations instead of common coordinate transformation are adopted.5. The reliable control problem for switched discrete-time linear systems is studied without the requirement of the solvability conditions for the reliable control problem of subsystems. The first part deals with the reliable control problem for the system with faulty actuators by using multiple Lyapunov functions method. For each subsystem of such a switched system, an observer and an observer-based reliable controller are designed. A switching rule depending on the observer state is designed which, together with the controllers, guarantee the stability of the closed-loop switched system for all admissible actuator failures. The second part studies the problem of reliable H? filtering for a class of switched discrete-time time-delay systems with sensor failures. Sufficient conditions are provided to guarantee asymptotic stability of the switched filtering error systems with H? performance y for all possible sensor failures via multiple Lyapunov functions approach. Then, with Finsler's lemma, reliable H? filtering and estimated state-dependent switching law design conditions are derived. The corresponding filter gains and switching law can be obtained from these conditions for some given scalar. The proposed method reduces design conservatism by introducing some slack variables.The conclusions and perspectives are presented in the end of the thesis.