On Stabilization Of Switched Systems With Unstable Subsystems

Switched system,as an important model in system control science,is an international frontier research field of the system control theory.It consists of a family of subsystems and a switching law governing the switching among them.Up to now,the stability of switched systems is still a hot subject for researchers.However,most of the existing results are concerned with switched linear or nonlinear systems with all stable subsystems,thus conservatism is inevitable.As we know,a switched system with all stable modes may be unstable under inappropriate switching,while a switched system with all unstable modes may be stable if we choose a proper switching law.Thus,the introduction of the switching rule greatly enriches the dynamic behavior of control system.In practical engineering,the unstable subsystems are often encountered,thus we need to design appropriate switching rules to make the system stable.For switched systems,which consists some or all unstable subsystems,this thesis considers the stabilization problem in the following aspects:First,the finite-time stabilization of switched nonlinear systems in the presence of unstable modes is studied.Following the idea that the effects of stable modes compensate to the bad effects of unstable modes,and utilizing the mode-dependent average switching frequency strategy,a switching law is designed to guarantee the finite-time stability of switched systems.Second,the asymptotic stabilization problem for discrete-time switched systems with all unstable modes is investigated.Following the idea of getting into each unstable mode and analyzing its internal behavior,the state dynamical decomposition technique is used to convert such a problem to an equivalent one for the inter-decoupled switched systems.Moreover,a periodical switching law is designed to guarantee the asymptotic stability of switched systems.Finally,the finite-time stability problem of discrete-time switched singular systems consisting of a family of unstable modes is analyzed.By means of dynamic decomposition technique,the original singular system is converted to a reduced-order normal discrete-time switched system.Two approaches,namely,the Lyapunov one and the state transition matrix one,are utilized to design the switching law with modedependent average dwell time such that the finite-time stability property is guaranteed.