Skip to main content
SpringerLink
Log in

Exponential polystability of separable motions

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We establish conditions of exponentialx 1-stability and polystability for systems with separable motions. Stability conditions of these types are obtained by using the Lyapunov functions (scalar and matrix).

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

Similar content being viewed by others

References

  1. A. B. Aminov and T. K. Sirazetdinov, “Method of Lyapunov functions in problems of polystability of motion,”Prikl Mat. Mekh.,51, No. 5, 709–716 (1987).

    MathSciNet  Google Scholar 

  2. A. A. Martynyuk, “A theorem on polystability,”Doki Akad. Nauk SSSR,381, No. 4, 808–811 (1991).

    Google Scholar 

  3. A. A. Martynyuk, “A new trend in the method of Lyapunov matrix functions,”Dokl Akad. Nauk SSSR,319, No. 3, 554–557 (1991).

    Google Scholar 

  4. A. A. Martynyuk and L. N. Chernetskaya, “On polystability of linear autonomous systems,”Dokl Akad. Nauk Ukr.SSR, Ser.A, No. 8, 17–20 (1993).

    Google Scholar 

  5. A. A. Martynyuk and L. N. Chernetskaya, “On polystability of linear systems with periodic coefficients,”Dokl. Akad. Nauk Ukr.SSR, Ser.A, No. 11, 61–65 (1993).

    Google Scholar 

  6. A. A. Martynyuk, “On exponential polystability of separable motions,”Dokl. Akad. Nauk Rossii,360, No. 4, 446–447 (1994).

    Google Scholar 

  7. A. A. Martynyuk, “On polystability of motions with respect to a part of variables,”Dokl. Akad. Nauk Rossii,324, No. 1, 39–41 (1992).

    Google Scholar 

  8. A. A. Martynyuk, “On exponential stability with respect to a part of variables,”Dokl. Akad. Nauk Rossii,331, No. 1, 17–19 (1993).

    Google Scholar 

  9. Jianxun He and Muson Wang, “Remarks on exponential stability by comparison functions of the same order of magnitude,”Ann. Different. Equal.,7, No. 4, 409–414 (1991).

    MATH  MathSciNet  Google Scholar 

  10. W. Hahn,Stability of Motion, Springer, Berlin 1967.

    MATH  Google Scholar 

  11. A. A. Martynyuk, “On the Lyapunov matrix function and stability of motions,”Dokl. Akad. Nauk SSSR,280, No. 5, 1062–1066 (1985).

    MathSciNet  Google Scholar 

  12. A. A. Martynyuk, “The Lyapunov matrix function,”Nonlin. Anal., No. 8, 1223–1226 (1984).

    Google Scholar 

Download references

Authors
  1. A. A. Martynyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Martynyuk, A.A. Exponential polystability of separable motions. Ukr Math J 48, 715–724 (1996). https://doi.org/10.1007/BF02384238

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02384238

Keywords

Search

Navigation