| The switched system has attracted great attention in the control systems community in recent years. The research of switch-ed systems has drawn a considerable attention and a lot of nice results have been obtained for switched linear systems. However the results have obtained for switched nonlinear systems are less than that of switched linear systems. Switched and hybrid Hamilton systems is a kind of important hybrid systems which exists many practical hybrid physical systems such as electric systems, power systems and machine systems, etc. This is because switched and hybrid systems not only are very challenging in their theoretical development, but also play an considerable role in many practical control systems which need switching among different model structures in their operation processes, for example, power systems in the process of emergency control, etc. Since there are few results obtained for switched linear Hamiltonian systems, there are fewer results proposed for switched nonlinear Hamiltonian systems. Therefore, all of the results obtained for switched and hybrid nonlinear Hamiltonian systems in this dissertation are new and different than the results proposed for switched systems before.This dissertation investigates the stability analysis and control design of three kinds of switched and hybrid systems as follows: (i) switched dissipative Hamiltonian systems with finite number of switching subsystems, (ii) hybrid dissipative Hamiltonian systems with infinite number of switching subsystems, and (iii) one-dimensional switched Hamiltonian systems with multiple equilibrium points, respectively. Many sufficient conditions of stability and asymptotical stability are first proposed for the three kinds of switched and hybrid dissipative Hamiltonian systems. Based on these, this dissertation then designs stabilization control, L2-disturbance control and H∞ robust adaptive control strategies for the systems. Thirdly, the results obtained in this dissertation are applied to general switched and hybrid systems via Hamilton realization, and many stability and control design results are presented for the systems. Based on the playground of the emergence control of power systems, a switched power system is built and investigated, and the stability result is given for the switched power system. The thesis is divided into eight chapters as follows.The first chapter first gives two surveys on the investigation status of the switched systems and the general dissipative Hamil-tonian systems respectively, then proposes the problem, objective and significance of the thesis.In chapter 2, this dissertation investigates the stability of the switched Hamiltonian systems with finite number of switching subsystems by means of different methods respectively, and proposes several stability/asymptotical stability results for the system. Applying the new results obtained, the corresponding stability and asymptotical stability results are also presented for ordinary switched systems with finite number of subsystems. The main results are listed as follows.1. To investigate the stability of switched Hamiltonian systems, an intuition assumption—Assumption 1 is first proposed. Assumption 1 means that all the Hamiltonian functions of the subsystems are increasing (or decreasing) along with increasing (or deceasing) of the P-normal of the system's state x. Under Assumption 1, several sufficient conditions of the stability and asymptotical stability are proposed for the system under arbitrary switching rules.2. Assumption 2, another assumption which more general than Assumption 1, is first presented. Assumption 2 means that all the Hamilton functions of the subsystems should have the same varying trend (simultaneously increasing or simultaneously decreasing). The stability result of the system is obtained by means of testing Assumption 2 satisfies the conditions of the Multiple Lyapunov Functions. A new asymptotical stability analysis method, called max-min energies method, is then proposed for the switched dissipative Hamiltonian systems. Using the new method and the dissipative Hamiltonian structural properties, several sufficient conditions are presented for the asymptotical stability of the switched Hamiltonian system under arbitrary switching paths.3. Zero-state detectability/observability are first investigated for the switched Hamiltonian system, and several sufficient conditions of uniform zero-state detectability/observability are proposed for the system. Based on the zero-state detectability/observability, the extended LaSalle's invariance principle is then presented for the switched Hamiltonian system. At last, several sufficient conditions are also proposed for the asymptotical stability results of the switched Hamiltonian system by means of the zero-state detectability/obserbality and extended LaSalle's invariance principle of the system.4. Based on the energy stability analysis method and the new results proposed in this paper, some useful corollaries are also presented for the zero-state detectability/observability, extended LaSalle's principle and asymptotical stability of ordinary switched nonlinear systems.Chapter 3 is to investigate the control design of switched dissi-pative Hamiltonian system with finite number of subsystems. Based on the zero-state detectability/observability, extended LaS-alle's invariance principle and stability results proposed in Chapter 2, the stabilization of the system is first studied, and two stabilizers are designed for the system under arbitrary switching paths. Secondly, the robust control design is investigated, and two types of controllers are designed for the system: one is a robust controller and the other is a robust adaptive one. Thirdly, the results obtained in this paper are used to study control design for ordinary switched nonlinear systems, and several useful results are presented. Finally, Study on examples with numerical simulations shows that the results obtained in this chapter are very practicable in the control design of switched systems.In Chapter 4, the stability analysis and control design are investigated for two types of hybrid Hamiltonian system with infinite number of subsystems, and several new stability and control results are proposed for the systems. The main results are listed as follows.1. The stability result is presented for System I—the values of switching law are infinite real number in a bounded and closed set in the real region. Based on this and zero-state detectabil-ity/observabiltiy of subsystem and the Hamiltonian structure properties, several sufficient conditions are proposed for the asymptotical stability of System I under restricted switched law. The sufficient condition of global asymptotical stability is also presented for the system under arbitrary switching laws.2. For System II—the value of the switching law depends on a piece-wise continuous function with respect to the state, several stability and asymptotical stability are also obtained by means of an appropriate transformation and the stability results of System I.3. The control design is investigated for System I, and the stabilizer and robust control law are proposed for the system.4. Based on the energy stability analysis and control design, the new results obtained in this chapter are applied to ordinary hybrid nonlinear systems with infinite number of subsystems, and several stability and control results are also proposed for the system.Chapter 5 is to investigate the problem of the region stability analysis and control design of one-dimensional switched Hamiltonian systems with multiple equilibrium points, and several sufficient conditions are proposed for the region stability of the system under arbitrary switching rules.In Chapter 6, we investigate the controllability and observability of switched linear systems, and propose some necessary and sufficient conditions for uniform controllability and observability of the systems.In Chapter 7, based on the emergence control of power systems, a model of switched power system is first built for the power system composing of two machine generators. The stability result is then proposed for the switched power system by using the new stability results obtained for the switched Hamiltonian systems.Conclusions and some problems to be studied further are in the eighth chapter.
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