Abstract: A non-fragile control method for the impulsive hybrid system, whose discrete part is described by a finite state machine (FSM), is presented. It can avoid the effect of the parameter uncertainty of the controller. By concerning the stability of two parts, a concept of asymptotical stability for the whole hybrid system is proposed. Then, based on the optimal road idea, the discrete state can visit the desired set infinitely often along the optimal road by controlling the firing of discrete event, i.e., the FSM is stabilized. In addition, by using the multiple Lyapunov function, under the assumption that the additive gain variation of controller is bounded, the control gain is determined to stabilize the continuous subsystem by solving an LMI. So, the whole hybrid system is stabilized. A simulation example shows the effectiveness of the proposed approach. This approach can be used for computer integrated manufacturing systems and traffic management systems.

Key words: uncertainty, impulsive hybrid systems, non-fragile control, multiple Lyapunov function