Simeonov, Pavel S.; Bainov, Drumi D. Orbital stability of the periodic solutions of autonomous systems with impulse effect. (English) Zbl 0684.34056 Publ. Res. Inst. Math. Sci. 25, No. 3, 321-346 (1989). Summary: The orbital asymptotic stability of the periodic solutions of autonomous systems with impulse effect is investigated. An analogue of the theorem of Andronov-Vitt is proved. Cited in 29 Documents MSC: 34D30 Structural stability and analogous concepts of solutions to ordinary differential equations 34C25 Periodic solutions to ordinary differential equations Keywords:orbital asymptotic stability; autonomous systems with impulse effect × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Mil’man, V. D. and Myshkis, A. D., On the stability of motion in the presence of impulses, Siberian Math. /., 1 (1960), 233-237 (in Russian). [2] Myshkis, A. D. and Samoilenko, A. M., Systems with impulses in prescribed moments of the time, Math. Sb., 74 (1967), 202-208 (in Russian) [3] Samoilenko, A. M. and Perestiuk, N. A., Stability of the solutions of differential equations with impulse effect, Differencial”nye Uravn. 11 (1977), 1981-1992 (in Russian). [4] , On the stability of the solutions of systems with impulse effect, Differencial’nye Uravn. II (1981), 1995-2001 (in Russian). [5] Simeonow, P. S. and Bainov, D. D., Asymptotic equivalence of two systems of differential equations with impulse effect, Systems & Control Letters 3 (1983), 297-301. · Zbl 0529.93050 · doi:10.1016/0167-6911(83)90029-4 [6] , Stability under persistent disturbances for systems with impulse effect, Journal of Math. An. and Appl. 109 (1985), 546-563. · Zbl 0579.34035 · doi:10.1016/0022-247X(85)90168-4 [7] , The second method of Liapunov for systems with an impulse effect, Tamkang Journal of Mathematics, 16 (1985), 19^0. [8] , Stability of the solutions of singularly perturbed systems with impulse effect, COMPEL. 5 (1986), 95-108. · Zbl 0636.34043 · doi:10.1108/eb010020 [9] , Stability with respect to part of the variables in systems with impulse effect, Journal of Math. An. and Appl., 117 (1986), 247-263. · Zbl 0588.34044 · doi:10.1016/0022-247X(86)90259-3 [10] Andronov, A. A. and Vitt, A. A., On the stability by Liapunov, Journ. of Exp. and Theor. Physics, 3 (1933) (in Russian). [11] Demidovich, B. P., Lectures on the Mathematical Theory of Stability, Nauka, Moscow, 1967. (in Russian). · Zbl 0155.41601 [12] Butenin, N. V., and Neimark, Yu. I. Fufaev, N. A., Introduction to the Theory of Nonlinear Oscillations, Nauka, Moscow, 1976 (in Russian). [13] Andronov, A. A, Vitt, A. A. and Khaikin, S. E., Oscillation Theory, Nauka, Moscow, 1981 (in Russian). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.