一类非线性混合系统的脉冲混合控制器设计

考虑了一类基于有限状态自动机的非线性混合动态系统，该混合系统由离散事件子系统和连续变量子系统构成。其离散事件子系统为有限状态自动机，连续变量子系统由几个具有脉冲的严格反馈非线性系统组成。结合有限状态自动机的相关理论、Backstepping方法以及脉冲控制设计了一种脉冲混合控制器，给出了整个系统在该控制器作用下渐近稳定的充分条件，构造混合多Lyapunov函数，并应用该函数和线性矩阵不等式(linear matrix inequality, LMI)技术证明了闭环系统渐近稳定性。最后,通过仿真实例验证了该方法的有效性。

Design of impulsive hybrid controllers for a class of nonlinear hybrid systems

A class of nonlinear hybrid dynamic systems based on finite state machine (FSM) is considered. The system comprises discrete event subsystem and continuous variable subsystem, the former is a finite state machine (FSM), and the latter consists of several strict feedback nonlinear systems. An impulsive hybrid controller for the nonlinear hybrid system is designed by applying FSM theory, Backstepping method and impulsive control. The sufficient condition of asymptotical stability of the whole system is presented. A hybrid multi-Lyapunov  function is also constructed, and the asymptotical stability result is proved by applying the function and linear matrix inequality (LMI) technique. Finally, a simulation example is given to show the effectiveness of the proposed method.