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**Orbital stability of the periodic solutions of autonomous systems with impulse effect.**
*(English)*
Zbl 0684.34056

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.

### MSC:

34D30 | Structural stability and analogous concepts of solutions to ordinary differential equations |

34C25 | Periodic solutions to ordinary differential equations |

### References:

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[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). |

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