On Necessary and Sufficient Conditions for the Asymptotic Stability of Impulsive Systems

We prove that the sufficient conditions for the asymptotic stability of impulsive systems obtained by Gurgula and Perestyuk are also necessary conditions.     

On the Stability of Periodic Impulsive Systems

In this paper, we consider periodic systems of ordinary differential equations with impulse perturbations at fixed points of time. It is assumed that the system possesses the trivial solution. We show that if the trivial solution of the system is stable or asymptotically stable, then it is uniformly stable or uniformly asymptotically stable, respectively. By using the method of Lyapunov functions, we establish criteria of uniform asymptotical stability and instability.     

Necessary and sufficient stability conditions for invariant sets of nonlinear impulsive systems

Necessary and sufficient conditions for the uniform asymptotic stability of the invariant set of a nonlinear impulsive system are established __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 132–142, February 2008.