Analysis And Control Of A Class Of Switched System

Hybrid systems are composed of discrete event dynamic systems and continuous time dynamic systems or discrete time dynamic systems, which interact on each other. Switched system is one of the most important branches of hybrid systems, and is essentially a nonlinear system. It consists of some linear subsystems that integrate the logical and continuous dynamics by switching. 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. 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 optimal control for the discrete linear switched systems. In last part, the switching controller is designed for the inverted pendulum systems. The work involved is as follows: (1) The stability analysis for a class of the discrete linear switched system is given, and the state feedback stabilization is also presented. Based on Lyapunov stability theory, using the Lyapunov function method and the least switching strategy, a sufficient condition for the stabilization of closed-loop system is given. Based on these, a switching strategy and sub-controllers are presented. If the switching interval time is constrained, the switching strategy and sub-controllers can also guarantee the closed-loop system is asymptotically stable. If the state value can not be measured directly, the switching strategy and sub-controllers, which use the observer value, are designed to guarantee the closed-loop system is asymptotically stable. (2) The robust control design for a class of discrete linear switched system with subsystem parameters uncertainty is given. The parameter uncertainties comply with certain kind of precondition, which guarantee the system has the common Lyapunov function. The switching strategy and sub-controllers are designed to guarantee the closed-loop system is asymptotically stable. In the next place, the state feedback H∞control is studied for a class of discrete linear switched system with disturbance. A sufficient condition for the existence of sub-controllers is presented, the switching strategy and sub-controllers are designed to guarantee the closed-loop system is asymptotically stable. (3) With the periodic-type switching strategy, the stability analysis and optimal control for a class of discrete linear switched system is given. A sufficient condition for the stabilization of switched system is presented. The problem can be resolved by converting the target function norm into its maximum eigenvalue. Combined with the stabilization condition, the optimal switching strategy is presented. (4) The switching control is applied in the inverted pendulum and simulation is made for design method. The switching controller consisting of stabilization controller and induced controller is designed for the linear single inverted pendulum system. Based on the Lyapunov function method, the stabilization region is presented. In the case of system states within the stabilization region, the closed-loop system can be asymptotically stable by the stabilization controller, otherwise, system states can be induced by the induced controller to the stabilization region, then switched to stabilization controller.