Stability analysis of systems with impulse effects

We establish sufficient conditions for the uniform stability and the uniform asymptotic stability of an equilibrium of systems with impulse effects described by systems of nonlinear, time varying ordinary differential equations. Under some additional mild assumptions, these sufficient conditions turn out to be necessary as well. For the case of time-invariant systems with impulse effects described by nonlinear ordinary differential equations, the above results are used to establish conditions under which the uniform asymptotic stability of an equilibrium can be deduced from the linearizations of such systems.