Stability Analysis and Controller Design for Discrete-Time Switched System
|School||Harbin Institute of Technology|
|Course||Control Science and Engineering|
|Keywords||Discrete-time switched linear systems Switched Lyapunov function Linear matrix inequality Norm-bounded uncertainty|
Hybrid systems, which are consisted of continuous and discrete dynamics interacting under certain logical rules, have gained considerable attention recently in science and engineering. As an important branch and an abstract concept of hybrid systems, switched systems there has drawn increasing interest because they provide a natural and convenient unified framework for mathematical modeling of many complex physical phenomena and practical applications. Typical switched system is composed of a family of subsystems and a switching signal that orchestrates the switching among them. Although each subsystem is very simple, the whole system that consists through switching strategy maybe have very complex dynamic characteristics. Today, switched systems theory and switched control strategy have been widely applied in many fields such as electrics, aerospace and astronautics, network communication, chemical engineering and so on. This dissertation deals mainly with theoretical analysis and computer simulation. Based on Lyapunov stability theory, this dissertation investigates the stability analysis, the robust control and application of the theory for the discrete linear switched systems. The work involved is as follows:Chapters 1-2 firstly introduce and review the state of the art in switched systems. We summarize the difference and relationship of switched systems with others which contain switching characteristic. Then we introduce some preliminary mathematic theory knowledge which will be useful for later explanation.Chapter 3 investigates the stability problems of the discrete-time uncertainty switched systems. To begin with, we summarize the several typical forms of Lyapunov function approach in stability analysis issue and their qualities on conservativeness and applicableness in stability analysis for switched systems. Based on switched Lyapunov function, the stability condition is given for the switched system in which the state value can not be measured directly, and then the sub-controllers, which use the observer value, are designed to guarantee the closed-loop system is asymptotically stable. Chapter 4 investigates the problems of controller design for uncertain discrete-time switched linear systems. Based on switched Lyapunov functions, the H∞and L2-L∞performance criteria are presented for discrete-time switched linear systems with norm-bounded uncertainties. And then we address an output feedback controller under arbitrary switching signals, in which a H∞and L2-L∞performance are required. The condition is shown in the form of linear matrix inequalities (LMI). Finally, a numerical example shows the feasibility of the designed controller.Chapter 5 based on the previous works, concerned with the state feedback guaranteed cost problem for a class of discrete-time switched system with both time delay and norm-bounded uncertainty. By applying switched Lyapunov function which renders the results to be potentially less conservative, state feedback controller is derived in term of LMI. Furthermore, the guaranteed cost control design problem is turned into a convex optimization problem with LMI constrains, which minimizes the guaranteed cost of the closed-loop switched system. A numerical example is provided to show the advantages of the proposed techniques.Chapter 6 investigates the problems for designing of BTT missile’s pitch/yaw channel autopilot based on the switched system theory. Based on the analysis method of chapter 5 in this dissertation, the guaranteed state feedback controller is designed in term of LMI. And then based on the eigenvalue-structure assignment method in reference, a forward-back controller is derived. Finally, simulation results demonstrate the validity of the proposed method in asymptotically stable and command tracking.