Finite time stability of a class of hybrid dynamical systems

This note considers the finite time stability of a class of hybrid dynamical systems, which has both switching and impulsive effect. First, by relaxing the restriction on Lyapunov function of the system, a new condition of finite time stability is given for non-linear systems. Then, this condition and the results of previous works (Bhat and Bernstein, 2000; Moulay and Perruquetti, 2003) are extended to study the finite time stability of a class of hybrid dynamical systems, several sufficient conditions are derived. Finally, a numerical example is given to illustrate the theoretical results.