Skip to main content
SpringerLink
Log in

Representation of solutions of hybrid difference-differential systems

  • Ordinary Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. März, R., Results Math., 2004, vol. 45, no. 1–2, pp. 88–95.

    MATH  MathSciNet  Google Scholar 

  2. Kirillova, F.M. and Strel’tsov, S.V., in Upravlyaemye sistemy: Sb. tr. In-ta matematiki SO AN SSSR (Control Systems. Collection of Works of Institute for Mathematics, Siberian Division, Academy of Sciences of USSR), Novosibirsk, 1975, issue 14, pp. 24–33.

  3. Akhundov, A.A., in Upravlyaemye sistemy: Sb. tr. In-ta matematiki SO AN SSSR (Control Systems. Collection of Works of Institute for Mathematics, Siberian Division, Academy of Sciences of USSR), Novosibirsk, 1975, issue 14, pp. 4–10.

  4. Trofimchuk, T.S., in Upravlyaemye sistemy: Sb. tr. In-ta matematiki SO AN SSSR (Control Systems, Collection of Works of Institute for Mathematics, Siberian Division, Academy of Sciences of USSR), Novosibirsk, 1980, issue 20, pp. 75–82.

  5. Shcheglova, A.A., Avtomat. i Telemekh., 2004, no. 11, pp. 86–101.

  6. Hybrid Systems: Prepr. 13th World Congr. IFAC, Gertler, J.J., Cruz, J.B., and Peshkin, M., Eds., 1996, vol. J, pp. 275–311, 473–476.

  7. de la Sen, M., Comput. Math. Appl., 1996, vol. 31, no. 1, pp. 109–122.

    Article  MATH  MathSciNet  Google Scholar 

  8. Vidal, R., Chiuso, A., Soatto, S., and Sastry, Sh., in Hybrid Systems: Computation and Control, Maler, O. and Pnueli, A., Eds., Berlin, 2003, LNCS 2623, pp. 526–539.

  9. Methods and Models in Automation and Robotics: Proc. of the 10th Intern. Conf. MMAR (30 August–2 September 2004), Domek, S. and Kasznyski, R., Eds., Poland: Miedzyzdroje, 2004, vol. 1, Control Theory, Control Engeneering, Modelling and Simulation.

    Google Scholar 

  10. van der Schaft, A. and Schumacher, H., An Introduction to Hybrid Dynamical Systems, Lecture Notes in Control and Inform. Sci., vol. 251, London: Springer-Verlag, 2000.

    Google Scholar 

  11. Marchenko, V.M., Tr. Inst. Mat. Akad. Nauk Belarusi, 2001, vol. 7, pp. 97–104.

    Google Scholar 

  12. Bellman, R. and Cooke, K., Differential-Difference Equations, New York, 1963. Translated under the title Differentsial’no-raznostnye uravneniya, Moscow: Mir, 1967.

  13. Hale, J., Theory of Functional Differential Equations, New York: Springer, 1977. Translated under the title Teoriya funktsional’no-differentsial’nykh uravenii, Moscow, 1984.

    Google Scholar 

  14. Marchenko, V.M. and Poddubnaya, O.N., Dokl. Akad. Nauk, 2005, vol. 404, no. 4, pp. 465–469.

    Google Scholar 

  15. Moiseev, N.N., Matematicheskie zadachi sistemnogo analiza (Mathematical Problems of Systems Analysis), Moscow: Nauka, 1981.

    Google Scholar 

  16. Marchenko, V.M. and Poddubnaya, O.N., in Problemy upravleniya i informatiki (Problems of Control Theory and Computer Science), Kiev, 2002, issue 6, pp. 17–25.

  17. Gabasov, R. and Kirillova, F.M., Kachestvennaya teoriya optimal’nykh protsessov (Qualitative Theory of Optimal Processes), Moscow: Nauka, 1971.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bialystok Technical University, Bialystok, Poland

    V. M. Marchenko & O. N. Poddubnaya

  2. Belarus State Technological University, Minsk, Belarus

    V. M. Marchenko & O. N. Poddubnaya

Authors
  1. V. M. Marchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. N. Poddubnaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © V.M. Marchenko, O.N. Poddubnaya, 2006, published in Differential’nye Uravneniya, 2006, Vol. 42, No. 6, pp. 741–755.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marchenko, V.M., Poddubnaya, O.N. Representation of solutions of hybrid difference-differential systems. Diff Equat 42, 789–804 (2006). https://doi.org/10.1134/S0012266106060036

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266106060036

Keywords

Search

Navigation