Stabilization, Tracking And H_∞ Control Of Cascade Nonlinear Switched Systems

Cascade nonlinear switched systems are an important class of hybrid systems, which have broad applications in engineering practice. Because of the inherent hybrid characteristic of switched systems, the complexity of nonlinear systems, and the interaction of the states of cascade systems, the dynamic behavior of the cascade nonlinear switched systems become very complicated. This makes the analysis and synthesis problems for the cascade nonlinear switched systems even more difficult. Few results focusing on such kind of switched systems have been reported up to now. This dissertation studies the stabilization, the tracking and the H_∞control problems ofseveral kinds of cascade nonlinear switched systems. The main contributions are as follows.The asymptotic stabilization problem for a class of cascade nonlinear switched systems with all interconnected parts in nonlinear form is studied. Sufficient conditions for the solvability of the stabilization problem are given using the common Lyapunov function method and the multiple Lyapunov function method respectively. State feedback controllers are designed respectively. Moreover, partial state-dependent switching laws are designed when the multiple Lyapunov function method is used.The quadratic stabilization problem for a class of cascade nonlinear switched systems with one interconnected part in linear form is studied. The problem is stuied using the hysteresis switching method and the min-projection method incorporated with the singal Lyapunov function method. In both cases, sufficient conditions for quadratic stabilization are given in LMIs forms, and sate-dependent switching laws and the state feedback controllers are designed.The H_∞control problem for a class of non-minimum phase cascade nonlinearswitched systems with all interconnected parts in nonlinear form is studied. The problem is studied using the common Lyapunov function method and the multiple Lyapunov function method respectively under different assumpations. Sufficient conditions for the solvability of the problem are given in both cases. The common Lyapunov function which independs on the solutions of the Hamilton-Jacobi inequalities and the multiple Lyapunov functions are constructed respectively. Moreover, state-dependent switching laws are designed when the multiple Lyapunov function method is used.The stability and L₂ -gain analysis problems for a class of cascade nonlinearswitched systems with both linear and nonlinear parts are studied respectively. In the cases that the zero dynamics are asymptotically stable under arbitrary switching laws and the zero dynamics is not stable under arbitrary switching laws, the average dwell-time and the state feedback controllers are designed respectively by using different strategies to the interconnected parts.The robust H_∞control problem for a class of uncertain affine nonlinear switchedsystems is studied. Sufficient conditions for the solvability of the problem are given in form of Hamilton-Jacobi inequalities. The state dependent switching laws and the dynamic output feedback controllers are designed such that the corresponding closed-loop system is locally asymptotically stable with a prescribed H_∞performancefor all the admissible uncertainties.The output tracking control problem for a class of cascade nonlinear switched systems is studied by using the average dwell-time method incorporated with variable structure sliding mode control strategy. Firstly, as a special case of output tracking control problem, we consider the stabilization problem for the system. Then, the result is extended to the output tracking control problem. Under different conditions, we consider the output tracking control problem with coordinate transformation and without coordinate transformation respectively. The common sliding surfaces are designed based on the Lyapunov design method. Then, the average dwell-times are designed considering the structural characteristic of the system, such that, when the stabilization problem is considered, all the states of the cascade nonlinear switched system can reach the sliding surface in a finite time interval and remain exponentially stable on it. When the output tracking control problem is considered, the output of the closed-loop system can track the desired signal exactly in a finite time interval and all the states of the system remain globally bounded thereafter.Finally, the results of the dissertation are summarized and further research problems are pointed out.