Quadratic Stability For Several Class Of Switched Systems

As a kind system of special and important in hybrid system, switched systemshave been favored by more and more scholars. Switched systems are composed ofsubsystems which are composed of a group of differential or difference equations anda switching rule. This particular system has been widely used in control theory andengineering practice. Quadratic stability of several important class of switchedsystems in hybrid systems are mainly discussed in this paper and combined with thesingle Lyapunov function method, S-procedure and so on. At the same time thetechnology of convex combination technique is used widely in this paper. Accordingto the characteristics of switched systems, the problems of quadratic stability withuncertain switched linear systems, uncertain switched linear systems with disturbanceinputs, multiple output linear switched systems and switched nonlinear systems withdisturbance inputs, described as follows:Hybrid systems, switched systems and the status quo of the research are brieflyintroduced in the first chapter. At the same time, the main research work of this paperis simply summarized. Then on the basis of quadratic stability of uncertain linearsystems, quadratic stability problem of uncertain linear switched systems is discussedwhen the systems are composed by two subsystems. Through the convex combinationtechnique, based on the approach single Lyapunov function method and S-procedure,a necessary and sufficient condition is given about quadratic stability of system andconvex combination system with a given switching law. Next chapter furtherresearches quadratic stability when the system exists disturbance. Under the premiseof in quadratic stability of convex combination system, uncertain linear switchedsystems with disturbance are the quadratic stability in the given inequality conditionthrough the design of switching law. Then next chapter studies quadratic stabilityproblem of the systems when there are measured output and regulated output. In thecase of the state feedbackH∞controller, the output feedbackH∞controller and thestate feedbackH2controller are existed in this systems, we discuss the quadratic stability of corresponding closed-loop system under certain switching laws after twothe conditions that establishment of quadratic stability of convex combinationcondition and the given inequality, respectively. The next chapter discusses quadraticstability of switched nonlinear systems with disturbance input. The relationshipbetween the quadratic stability of the switched nonlinear systems when there are twosubsystems and the quadratic stability of convex combination system are discussed inthis chapter by using single Lyapunov function method and designing switching law.Final part summarizes and reviews the whole article, prospecting problems to be furtherstudied.