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Stability analysis with respect to two measures of impulsive systems under structural perturbations

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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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References

  1. L. T. Grujić, A. A. Martynyuk, and M. Ribbens-Pavella, Large Scale Systems Stability under Structural and Singular Perturbations, Springer, Berlin (1987).

    Book  MATH  Google Scholar 

  2. W. Hahn, Stability of Motions, Springer, Berlin (1967).

    Google Scholar 

  3. A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore (1995).

    MATH  Google Scholar 

  4. S. Leela, “Stability of differential systems with impulsive perturbations in terms of two measures,” Nonlinear Anal., No. 1, 667–677 (1977).

  5. 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).

    Article  MathSciNet  Google Scholar 

  6. A. A. Martynyuk and V. G. Miladzhanov, “On stability of impulsive systems under structural perturbations,” Electron. Model., 16, No. 1, 3–7 (1994).

    Google Scholar 

  7. 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).

    Article  MATH  MathSciNet  Google Scholar 

  8. 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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Authors and Affiliations

  1. Institute of Mechanics, Ukrainian Academy of Sciences, Kiev

    A. A. Martynyuk

  2. University of Ioannina, Greece

    I. P. Stavroulakis

Authors
  1. A. A. Martynyuk
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  2. I. P. Stavroulakis
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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

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