Stability analysis of systems with impulse effects

In the present paper the authors establish conditions for the uniform stabi lity and the uniform asymptotic stability of equilibria of systems with imp ulse effects described by systems of nonlinear, time-varying ordinary diffe rential equations. Under mild additional assumptions, these sufficient cond itions turn out to be necessary as well. For the case of time-invariant sys tems,vith impulse effects described by nonlinear ordinary differential equa tions, the above results are used to establish conditions under which the u niform asymptotic stability of equilibria can be deduced from the lineariza tions of such systems.