Abstract
The asymptotic stability with respect to two measures of impulsive systems under structural perturbations is investigated. Conditions of asymptotic (ρ0, ρ)-stability of the system in terms of the fixed signs of some special matrices are established.
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L. T. Grujić, A. A. Martynyuk, and M. Ribbens-Pavella, Large Scale Systems Stability under Structural and Singular Perturbations, Springer, Berlin (1987).
W. Hahn, Stability of Motions, Springer, Berlin (1967).
A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore (1995).
S. Leela, “Stability of differential systems with impulsive perturbations in terms of two measures,” Nonlinear Anal., No. 1, 667–677 (1977).
A. A. Martynyuk, “A matrix-valued Lyapunov function and stability with respect to two measures of impulsive systems,” Rus. Acad. Sci. Dokl. Math., 50, No. 2, 330–334 (1995).
A. A. Martynyuk and V. G. Miladzhanov, “On stability of impulsive systems under structural perturbations,” Electron. Model., 16, No. 1, 3–7 (1994).
A. A. Martynyuk and I. P. Stavroulakis, “Stability analysis of linear impulsive differential systems under structural perturbations,” Ukr. Mat. Zh., 51, No. 6, 784–795 (1999).
Liu Xinzhi, “Stability results for impulsive differential systems with applications to population growth models,” Dynam. Stability Syst., No. 9, 163–174 (1994).
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Published in Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 11, pp. 1476–1484, November, 1999.
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Martynyuk, A.A., Stavroulakis, I.P. Stability analysis with respect to two measures of impulsive systems under structural perturbations. Ukr Math J 51, 1668–1680 (1999). https://doi.org/10.1007/BF02525270
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DOI: https://doi.org/10.1007/BF02525270