The Study Of Exponential Stability And H_∞ Control Of Singular Switched Systems

The switching phenomenon in the actual control system is universal. Traditional control system have been unable to adapt to the new complicated and diversified model of the dynamic systems,the generalized switching system arises at the historic moment.Switched systems are composed of multiple subsystems and a switching strategy between the various subsystems When partial or total subsystems are singular systems, the switched system becomes a class of switched singular systems. In the generalized switching system,Not only the initial conditions can cause impulse,The inconsistent state at the switching time can also cause impulse. The impulse is widespread in the control system, So there is great theoretical significance and practical value in studing the general switched systems with impulse effect.This thesis first studied the exponential stability problem of the generalized switching systems.Under the assumption that switching systems contain both stable and unstable systems and based on the Lyapunov stability theory,The sufficient condition of the exponential stability of the generalized switching system is given. To improve the traditional average dwell time method, puts forward the model dependent average dwell time method. On this basis,the exponential stability with a jump of generalized switching system are studied.By limiting the dwell time of the unstable subsystems and bordered the state jump at the switching time.Got a sufficient condition of exponential stability of generalized switching system with the impulsive effect.And based on this condition,a controller is designed, witch is used to calm the unstable subsystems of the generalized system.Considering that there are impulsive effect caused by the inconsistent initial condition, designed a hybrid impulse controller to eliminate the impulse.In the following, the H_∞ control problem of the singular switched systems are studied. First the definition of the H_∞ performance of singular switched systems are given. Based on multiple Lyapunov function method in combination with model dependent average dwell time switching signal,the sufficient condition of the H_∞ performance of singular switched systems with impulsive effect are obtained. Then a controller is designed to ensure the stable of each subsystem and eliminate the impulse when switch occurs according to the given conditions.