Stability Analysis And Feedback Stabilization Of Invariant Sets And Periodic Solutions Of A Class Of Hybrid Dynamical Systems  Posted on:20070306  Degree:Master  Type:Thesis  Country:China  Candidate:X Z Lin  Full Text:PDF  GTID:2178360212465526  Subject:Control theory and control engineering  Abstract/Summary:  PDF Full Text Request  As an important class of hybrid dynamical systems, a switched system is composed of several continuoustime subsystems or discretetime subsystems and the switching rules among them. During the last three decades or so, there is an increasing interest on the modeling, analysis, synthesis, and control of witched systems. Nowadays more and more attention has been paid to the study of switched systems.This dissertation devotes to the study of stability and feedback stbilization of invariant sets and closed orbits of switched systems. The main contributions of the research work presented in this dissertation are as follows:1 .An invariance principle is developed for a class of switched systems and the concept of the input tostate stability is extended to the case of the input to V ( x ) stability where V ( x ) is an energy function of the switched systems. Based on this notion and the invariance principle, the condition under which an invariant set of states of a switched system whose subsystems are Lyapunov stable can be stabilized by state feedback is proposed and proved. Finally, the relationship between the input to V ( x )stability and the input tostate stability is discussed in detail.2. The concept of the input/outputtostate stability is extended to the case of the input/outputto V ( x ) stability, which implies detectability of the zerovalue set of a storage function. Based on this notion and the passivity of nonlinear systems, we propose and prove the condition under which an invariant set of states of a switched system whose subsystems are all passive affine can be stabilized by output feedback. Finally, the relationship between the input/outputto V ( x )stability and the input/outputtostate stability is discussed in detail.3. The existence of closed orbits of 2dimension continuous switched systems is discused. We extended Dulac theorem comparing with Bendixson theorem and applied it to verify the existence of closed orbits of 2dimension continuous switched systems. Two examples are provided to illustrate the application of the obtained results. Based on the invariance principle we proved before, stabilization of limit cycles of the hybrid systems was investigated by JurdjevicQuinn method, and the asymptotically orbital stability of limit cycles under state feedback controllers was proved.  Keywords/Search Tags:  hybrid dynamical systems, switched systems, invariant set, feedback stabilization, input to V ( x )stability, input/outputto V ( x )stability, limit cycles, closed orbit, passivity, JurdjevicQuinn method, multiple Lyapunov functions  PDF Full Text Request  Related items 
 
