Asynchronous Control Of Impulsive Switched Systems

Switched systems, as a special class of hybrid system, have broad background of application. Switched systems consist of a switching rule and subsystems, where the switching rule orchestrates the running of subsystems. In practice, because of the changing environments, if a system works in a fixed mode, it usually can not reach the ideal control, and even instability. As a result, many real world control systems, such as aircraft control systems, embedded control systems, electric power systems use the “switching”idea to achieve the control objective. Therefore, the study of switched systems is significant for both practice and theory.Recently, lots of results about stability analysis, controller design and H∞ performance analysis have been obtained with the in depth study of switched systems. However, for a class of linear switched systems, some problems have not been solved. For example, when the system is switching between the subsystems, some phenomenons,such as asynchronous behaviors, impulsive effects may exist. These phenomenons usually add difficulties to the system analysis. By using Lyapunov stability theory, together with linear matrix inequalities technology, this thesis mainly investigates the stability analysis and synthesis of one kind of linear switched systems containing asynchronous behaviors or impulsive effects. With the definition of asymptotic or exponential stability, the stability problem for the continuous-time(discrete-time) linear switched systems with asynchronous behaviors or impulsive effects is studied. On the side of synthesis, the asynchronous H∞ control and filtering are studied. Besides, the stabilization of impulsive switched systems under asynchronous behaviors is investigated. The main studies of this paper are as follows:1. For a class of continuous-time linear switched systems with asynchronous behaviors, based on the average dwell time technology and Lyapunov functions method, the asymptotic stability and H∞ control results are obtained. With a proper transformation,the results are finally formulated in the form of linear matrix inequalities. Then, by using the toolbox in MATLAB, the controller gains are easily computed.2. Similar to the analysis of asynchronous H∞ control, the H∞ filtering problem of continuous-time linear switched systems with asynchronous behaviors is investigated under a switching constraint of average dwell time. With the help of the MATLAB software, the filter parameters are finally designed.3. For a class of switched systems with asynchronous behaviors and impulsive effects, the impulsive switched systems models are built. In order to reach the stabilization object, the asymptotic or exponential stability analysis is firstly studied with the method of Multiple Lyapunov functions, under a switching rule satisfying the mode-dependent average dwell time constraint. Then, the less conservative stabilization result is obtained based on the stability conclusion.