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Lipschitz quasistability of impulsive differential-difference equations with variable impulsive perturbations. (English) Zbl 0854.34073

Summary: By means of a suitable comparison lemma sufficient conditions for uniform Lipschitz stability of an arbitrary solution of an impulsive system of differential-difference equations with variable impulsive perturbations are obtained.

MSC:

34K20 Stability theory of functional-differential equations
34A37 Ordinary differential equations with impulses
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References:

[1] Dannan, F. M.; Elaydi, S., Lipschitz stability of nonlinear systems of differential equations, J. Math. Anal. Appl., 113, 562-577 (1986) · Zbl 0595.34054
[2] Kulev, G. K.; Bainov, D. D., Lipschitz quasistability of impulsive systems of differential equations, Internat. J. Theoret. Phys., 30, 1151-1162 (1991) · Zbl 0739.34017
[3] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S., Theory of Impulsive Differential Equations (1989), World Scientific: World Scientific Singapore · Zbl 0719.34002
[4] Bainov, D. D.; Covachev, V. C.; Stamova, I. M., Stability under persistent disturbances of impulsive differential-difference equations of neutral type, J. Math. Anal. Appl., 187, 790-803 (1994) · Zbl 0811.34057
[5] Bainov, D. D.; Dishliev, A. B., Quasiuniqueness, uniqueness and continuability of the solutions of impulsive functional differential equations, Rend. Mat. Ser. VII, 15, 391-404 (1995) · Zbl 0835.34015
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