Stabilization Of Some Classes Of Switched Nonlinear Systems

This thesis has investigated respectively that the problems of quadratic stabilization of multi-input multi-output switched nonlinear systems under arbitrary switching strategies, global stabilization of a class of multi-input cascade switched nonlinear systems under arbitrary switching strategies and H-infinity robust stabilization of a class of uncertain time-delay nonlinear systems. The main contributions are as follows.Firstly, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under arbitrary switching strategies is investigated. The concept of uniform normal form of this class of multi-input multi-output switched nonlinear systems is given, and the sufficient conditions for the existence of the uniform normal form and corresponding coordinate transformation are obtained. Furthermore, by means of the uniform normal form together with a common quadratic Lyapunov function of its zero dynamics, the quadratic stabilizability of multi-input multi-output switched nonlinear systems under arbitrary switching strategies is derived by designing state feedback control laws and constructing a common quadratic Lyapunov function of all the closed-loop subsystems. The results obtained are also applied to switched linear systems.Secondly, this dissertation considers the problem of global stabilization of a class of multi-input cascade switched nonlinear systems, which are composed of linear parts with control inputs and nonlinear parts with interconnections. When linear parts are minimum have uniform normal form, state feedback control laws are designed, which make linear parts quadratically stable under arbitrary switching strategies. At the basis of the previous works, appropriate technical treatments of the nonlinear parts are given, the global asymptotic stability of the whole closed-loop switched nonlinear systems under arbitrary switching strategies are realized by constructing a composite common Lyapunov function.Finally, this thesis investigates the problem of H-infinity robust stabilization of a class of uncertain time-delay nonlinear systems via hybrid state feedback strategy. Suppose that there exist finite candidate state feedback controllers, and none of the individual controllers can guarantee the systems H-infinity robust stable. When the gain matrices of controllers are all known, by using single Lyapunov function method and convex combination technique, the sufficient conditions of the closed-loop switched nonlinear systems with robust H-infinity performance are derived and the corresponding switching strategy is designed. when the gain matrices of controllers are unknown, by employing multiple Lyapunov function method, the controllers and the corresponding switching strategy are designed to make the closed-loop switched nonlinear systems be robust H-infinity asymptotically stable.