Instability of dynamical systems subjected to impulsive actions.

We investigate the instability property of finite dimensional impulsive systems by means of Lyapunov-like tools. Auxiliary functions of Chetaev type are used. Sufficient conditions restricting the time intervals between impulsive actions guaranteeing the instability are provided. These conditions cover in particular the case where both discrete and continuous dynamics are stable. By means of an example we demonstrate that even in this case the instability can take place.