Geodesic
On the Stability of Periodic Impulsive Systems
Matematičeskie zametki, Tome 76 (2004) no. 1, pp. 44-51.

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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. 
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R. I. Gladilina; A. O. Ignatyev. On the Stability of Periodic Impulsive Systems. Matematičeskie zametki, Tome 76 (2004) no. 1, pp. 44-51. http://geodesic.mathdoc.fr/item/MZM_2004_76_1_a4/

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