Robust Stabilization And Disturbance Attenuation Properties For Switched Nonlinear Systems With Lower Triangular Form

As a special type and important class of hybrid systems, a switched system is of great significance both in theory research and engineer applications. Therefore, the study of switched systems has attracted increasing attention. The behavior of switched systems is very complicated because of the interaction between the continuous dynamics and discrete switching signals. So there are still many open problems which need to be studied. In addition, the research results of switched systems are also significant reference to hybrid systems in terms of theories and methods. As the basic problems of nonlinear control systems, both the stabilization and the disturbance attenuation properties of switched systems are challenging problems.The Lyapunov theory, backstepping technique and the adding one power integrator technique are the major methods adopted in the study, and some other theories and methods of both switched systems and nonlinear control systems are also applied and extended to study the global robust stabilization and the disturbance attenuation properties for a class of switched nonlinear systems with lower triangular form. Based on multiple Lyapunov functions and dynamical dwell time, the stabilization and the robust stabilization are addressed for switched nonlinear systems with nested lower triangular form and uncertain switched systems with nested lower triangular form respectively. The disturbance attenuation properties are based on multiple Lyapunov functions and average dwell time. Meanwhile, the global robust stabilization is studied for high-order lower-triangular switch systems.The main contributions of this thesis can be summarized as follows.Firstly, we study the global stabilization and the global robust stabilization for a class of switched nonlinear systems with nested lower triangular form without uncertainty and with uncertainties respectively. The Lyapunov function and the state feedback controller for each subsystem will be simultaneously constructed by backstepping. Based on the multiple Lyapunov functions, a switching signal about dynamical dwell time is designed, which guarantees the closed-loop switched nonlinear system is global stable. According to the method above, the global robust stabilization will be considered for a class of uncertain switched nonlinear systems with nested lower triangular form. The uncertainties need to satisfy the norm-bounded conditions.Secondly, we consider the problem of disturbance attenuation with stability for a class of switched nonlinear systems with nested lower triangular form. The state feedback controller for each subsystem and the Lyapunov function will be derived explicitly by backstepping. Under the switching signal of average dwell time, the closed-loop switched system has the weight disturbance attenuation from the disturbance input to the controlled output.Thirdly, we address the robust stabilization for a class of switched nonlinear systems with high-order lower triangular form. All subsystems considered are feedback non-linearizable and non-affine in the control variables. Based on the method of adding one power integrator, the feedback control law and the Lyapunov function will be designed for each subsystem. The closed-loop switched nonlinear systems will be global robust approximation stabilize under the designed switching signal.Finally, we summarize the whole dissertation and discuss the further research work.