A system of linear differential equations with pulse action at fixed times is considered. We obtain sufficient conditions for the existence of a positive-definite quadratic form whose derivative along the solutions of differential equations and whose variation at the points of pulse action are negative-definite quadratic forms regardless of the times of pulse action.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 11, pp. 1451–1458, November, 2010.
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Ignat’ev, A.O. On the existence of a lyapunov function as a quadratic form for impulsive systems of linear differential equations. Ukr Math J 62, 1680–1689 (2011). https://doi.org/10.1007/s11253-011-0460-9
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DOI: https://doi.org/10.1007/s11253-011-0460-9