Analysis And Synthesis Of Switched Systems Based On Mode Dependent Dwell Time

In real objects and processes, many of their dynamic behavior are coupled by continuous dynamic systems and discrete events. In the academic field, it is called as hybrid system. Hybrid system is an interdisciplinary subject, primarily applied mathematics,control engineering and computer science. From the perspective of control theory, hybrid systems are generally modeled into switched systems.During the past decades, due to the structure of systems increasingly complex, the operation mechanism of system is restricted by many factors. To get a better solution,many engineering and theory problems must adopt switched system theory, thus switched system has become a hot topic both in the academic and engineering. The dynamic behavior of switched system not only depends on each subsystem, but also closely related to switching law. Besides, the actual switched systems may have unstable subsystems,strong nonlinear, time delay and external or internal disturbance etc. As a consequence,the stability analysis and controller synthesis of switched systems are more complex compared to the general control systems.The stability analysis and controller synthesis of the switched system with unstable subsystems are mainly studied in this thesis. By combining the Lyapunov stability theory,some works are carried out on the stability analysis and controller synthesis problems of switched system with unstable subsystems by mode dependent average dwell time technology. The main works considered in this thesis are listed as follows:1. First of all, for continuous time switched system with unstable subsystem, two kinds of switching strategies are presented, namely the slow switching and fast switching. Under two different switching strategies, the stability problem of continuous time switched system is studied, less conservative and more decidable conditions are acquired.And the corresponding results can be extended to the switched nonlinear system.2. Based on the stability conditions of the continuous time switched system, the research object is extended to discrete time switched system. Under two switching strategies, the stability conditions of discrete time switched systems with unstable switching subsystem is obtained, respectively. And the results are less conservative, more likely to judge.3. Finally, take the discrete time switched nonlinear system as an example, by using the T-S fuzzy modeling method, the controllers of discrete time switched nonlinear systems under asynchronous switching are finally synthesized in this paper on the basis of the stability conclusions obtained in consideration of the situation that subsystems controllers don’t match to the corresponding subsystems.To sum up, the innovation of this thesis lies in:On the one hand, for the first time, two switching strategies, slow switching and fast switching, are put forward for switched switched with unstable subsystems, which lead to the switching schemes of switched systems more flexible.On the other hand, the less conservative stability conditions are acquired based on the mode dependent average dwell time technology.All the results mentioned above are solved and verified by the LMI toolbox of Matlab. The simulation results show that the analysis and synthesis of switched system based on mode dependent average dwell time techniques is effective.