Nonlinear Oscillations

, Volume 9, Issue 3, pp 375–390 | Cite as

Approximation of a bundle of solutions of linear differential inclusions

  • N. V. Plotnikova


We construct an approximation of a bundle of solutions of a linear impulsive differential inclusion using a system of linear impulsive differential equations with Hukuhara derivative.


Support Function Differential Inclusion Multivalued Mapping Subsequent Decomposition Hukuhara Derivative 
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  1. 1.
    A. I. Panasyuk and V. I. Panasyuk, Asymptotic Optimization of Nonlinear Systems of Control [in Russian], Byelorussian University, Minsk (1977).Google Scholar
  2. 2.
    A. A. Tolstonogov, Differential Inclusions in a Banach Space [in Russian], Nauka, Novosibirsk (1986).MATHGoogle Scholar
  3. 3.
    J.-P. Aubin, “Mutational equations in metric spaces,” Set-Valued Analysis, 1, No. 1, 3–46 (1993).CrossRefMathSciNetGoogle Scholar
  4. 4.
    F. L. Chernous'ko, Estimation of a Phase State of Dynamical Systems. Method of Ellipsoids [in Russian], Nauka, Moscow (1988).Google Scholar
  5. 5.
    A. L. Dontchev, Perturbations, Approximations, and Sensitivity Analysis of Optimal Control Systems, Springer, Berlin (1983).MATHGoogle Scholar
  6. 6.
    V. A. Plotnikov, A. V. Plotnikov, and A. N. Vityuk, Differential Equations with Multivalued Right-Hand Side. Asymptotic Methods [in Russian], Astroprint, Odessa (1999).Google Scholar
  7. 7.
    M. S. Nikol'skii, “On one method for the approximation of the reachability set for a differential inclusion,” Zh. Vyshisl. Mat. Mat. Fiz., 28, No. 8, 1252–1254 (1988).Google Scholar
  8. 8.
    V. Veliov, “Second order discrete approximations to linear differential inclusions,” SIAM J. Numer. Anal., 29, 439–451 (1992).CrossRefMathSciNetGoogle Scholar
  9. 9.
    F. S. de Blasi and F. Iervolino, “Equazioni differenziali con soluzioni a valore compatto convesso,” Boll. Unione Mat. Ital., 2, Nos. 4–5, 491–501 (1969).Google Scholar
  10. 10.
    V. I. Blagodatskikh and A. F. Filippov, “Differential inclusions and optimal control,” in: Topology, Ordinary Differential Equations, and Dynamical Systems [in Russian], Vol. 2, Nauka, Moscow (1985), pp. 194–252.Google Scholar
  11. 11.
    F. S. de Blasi and F. Iervolino, “Euler method for differential equations with set-valued solutions,” Boll. Unione Mat. Ital., 4, No. 4, 941–949 (1971).Google Scholar
  12. 12.
    N. V. Plotnikova, “Approximation of a bundle of solutions of linear impulsive differential inclusions,” Visn. Kharkiv Nats. Univ., Ser. Mat. Prikl. Mat. Mekh., Issue 54, 67–78 (2004).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • N. V. Plotnikova
    • 1
  1. 1.Odessa National UniversityOdessa

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