Finite time stability and stabilization of impulsive dynamical control systems

Impulsive dynamical system consists of continuous dynamics and discrete dynamics. It is possible to control the trajectories of impulsive dynamical systems to an equilibrium state in finite time by either the continuous dynamics or discrete dynamics or both of them. In this paper, we investigate the finite-time stability and stabilization of impulse dynamical control systems. We develop two sufficient conditions for finite-time stability of impulsive dynamical systems, which emphasize the effects of discrete dynamics and continuous dynamics on finite-time stability respectively. Based on these sufficient conditions, we design impulse or continuous control strategies for two class of impulsive dynamical control systems. Two numerical examples are also given to illustrate these control strategies.