This paper focuses on the stability analysis and invariant set stability theorems for nonlinear impulsive systems. A set of Lyapunov-based sufficient conditions are established for these convergent 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 make it possible to deduce properties of the functions and thus leads to sufficient conditions for convergence and stability.