Semistability for nonlinear impulsive systems

In this paper we develop the stability analysis and invariant set stability theorems for nonlinear impulsive systems. Two notions that are of articular relevance to such systems are convergence and semistability. We relate convergence and stability to the classical concepts of system storage functions to impulsive systems providing a generalized hybrid system energy interpretation in terms of stored energy. we show that a set of Lyapunov-based sufficient conditions for establishing these convergent properties. These makes it possible to deduce properties of the Lyapunov function and thus leads to sufficient conditions for convergence, stability and semistability. Finally, the efficacy of the main results is shown by a numerical example.