Lyapunov condition and semistability of impulsive systems

This paper focuses on the stability analysis and invariant set stability theorems for nonlinear impulsive systems. we show that a set of Lyapunov-based sufficient conditions for establishing convergence and semistability properties. These results do not require the Lyapunov function to be positive definite. Inequalities relating the righthandside of the differential equation and the Lyapunov function derivative are involved for these results. These inequalities makes it possible to deduce properties of the storage functions and thus leads to sufficient conditions for convergence, stability and semistability. Finally, a numerical example is provided to demonstrate the efficacy of the main results.