Analysis And Synthesis For A Class Of Discrete-time Switched Systems

As an important class of hybrid systems, a switched system is composed of several continuous time subsystems or discrete time subsystems and the switching signal among them. With its own particularity, it is different from the continuous time systems or discrete time systems. Although each subsystem is very simple, the whole system that consists through switching strategy maybe have very complex dynamic characteristics. Simple switching between two stable subsystems would cause unstable dynamics, while appropriate switching between two unstable subsystems would also make the system stable. Therefore, researching on the switched systems is full of theoretical sense and application value, and now, it is a hot issue in control field.Based on Lyapunov stability theory together with linear matrix inequality technique, this dissertation investigates the discrete-time switched systems. The work involved is as follows:(1) Quadratic Stability of Switched Systems consisting of a class of m-discrete subsystems is studied. An interval matrix is constructed to transform the discrete switched system into interval system. Then, a sufficient condition is presented in terms of matrix inequality for the quadratic stability of discrete switched systems under any switching laws. This condition is much simpler than the other methods because it needs only one matrix inequality to solve.(2) A class of discrete time switched systems with parametric uncertainty is considered, and the robust stability problem and disturbance attenuation problem are studied forth is class of system s under arbitrary switching. Sufficient conditions for the switched systems to be robustly stable with H∞disturbance attenuation are obtained using multiple Lyapunov function technique, and these conditions can be formulated via linear matrix inequalities (LMIs).(3) For a class of discrete-time state delay switched systems with parameter uncertainty, this paper addresses the problem of designing the guaranteed cost state feedback controller of quadratic stabilization under arbitrary switching laws. A condition for the existence of guaranteed cost controllers is derived. This condition can be solved easily with the MATLAB LMI toolbox. (4) For a class of discrete-time delay switched systems with norm bounded parameter uncertainty and a quadratic cost index, the problem of designing a suboptimal guaranteed cost state feedback controller is considered. A sufficient condition on the existence of robust guaranteed controllers is derived by using a piecewise Lyapunov function approach together with linear matrix inequality technique, and the parameterized representation of the controllers is given in terms of linear matrix inequalities. Based on that, the design problem of the suboptimal guaranteed cost controller is turned into a convex optimization problem with linear matrix inequalities constraints.