Geodesic
Asymptotic stability and instability of the solutions of systems with impulse action
Matematičeskie zametki, Tome 80 (2006) no. 4, pp. 516-525

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In this paper, we study the stability of the zero solution of a system of ordinary differential equations subject to impulse action. Using the method of Lyapunov functions, we obtain tests for asymptotic stability or instability of the system. Illustrative examples are given. 
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     author = {A. O. Ignatyev and O. A. Ignatyev and A. A. Soliman},
     title = {Asymptotic stability and instability of the solutions of systems with impulse action},
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A. O. Ignatyev; O. A. Ignatyev; A. A. Soliman. Asymptotic stability and instability of the solutions of systems with impulse action. Matematičeskie zametki, Tome 80 (2006) no. 4, pp. 516-525. http://geodesic.mathdoc.fr/item/MZM_2006_80_4_a4/