Abstract:

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.