Stability Analysis And Control Of Several Classes Of Hybrid Dynamical Systems

Hybrid dynamical systems are the complicated systems that consist of continuous (or discrete) time dynamics, discrete event (or logical) dynamics, and the interaction between them. Hybrid dynamical systems can provide an effective framework for mathematical modeling and analysis of many complex physical phenomena and practical applications. They have a variety of applications such as hybrid automata, sampled-data control systems, aircraft control system, automotive control systems and network control systems etc. Thus, the study of hybrid dynamical systems has important significance both in theory and applications.In this dissertation, stability analysis and control problem of several classes hybrid dynamical systems are studied. The main contributions and original ideas included in the dissertation are summarized as follows.1.The stability of a class of hybrid dynamical systems is studied. By combining the advantages of multiple Lyapunov functions and vector Lyapunov function, multiple vector Lyapunov functions (MVLF) is proposed. By using the MVLF, we weaken the hypothesis on the Lyapunov function of systems, and give a sufficient condition of asymptotic stability for the systems. A simulation is given to illustrate the effectiveness of the proposed method.2.The practical stabilization of a class of hybrid dynamical systems is studied. These hybrid dynamical systems have time-varying subsystems and time-varying state jump. Firstly, by using the state jump function, we determine a strict increased switch- ing sequence for the system. Then, for each time interval of the switching sequence, we explicitly construct a corresponding linear state feedback control laws, which practically stabilize the closed-loop systems.3.The finite time stability and stabilization of a class of hybrid dynamical systems are studied. At first, by relaxing the restrictions on Lyapunov function of the system, a new necessary and sufficient condition of finite time stability is given for nonlinear system. Then, we present the concept of finite stability for hybrid dynamical systems. By using the condition mentioned above and the results of previous works (Bhat & Bernstein, 2000; Moulay & Perruquetti, 2003), we further study the finite time stability of hybrid dynamical system, several sufficient conditions are derived. Finally, based on the state partition of continuous and resetting parts of system, a hybrid feedback controller is constructed, which stabilizes the closed-loop systems in finite time. 4.Based on the finite state machine (FSM), the stability and stabilization of hybrid dynamical systems are studied. Firstly, by concerning the stability of two parts, a concept of asymptotical stability for the whole hybrid dynamical systems is proposed. Moreover, a new stability criterion is given. Then, based on the hybrid observer, we further construct a hybrid feedback controller, which asymptotically stabilize the closed-loop system. Finally, we extend the results obtained above to the uncertain hybrid dynamical systems, where uncertainties appear in the place jump of FSM, the parameter of continuous subsystems and the parameter of controller. Based on optimal road idea, we construct a non-fragile controller by solving an LMI, which asympto- tically stabilize the closed-loop system.5. Based on the (extended) differential Petri net (DPN), the stability of hybrid dynamical systems is studied. At first, according to the characteristics of hybrid dynamical systems, we propose its differential Petri net model, and give the concept and lemma of stability for DPN. Then, by using two auxiliary functions G , and the information of index matrix, we construct a new hybrid Lyapunov function and present the stability theorem for DPN. On the other hand, by relaxing the restriction on the enabling condition depends on the weight of arc, and extending the definition of weight for arc, extended differential Petri net (EDPN), a new model tool, is proposed. EDPN adopts both the advantages of generalized differential Petri nets and hybrid automata. Using this model, a sufficient condition of asymptotic stability for hybrid dynamical systems is obtained by combining the stability of two parts. In addition, by using the information of index matrix and a new hybrid Lyapunov function, the stability theorem of linear HDS is obtained. H...