Skip to main content
SpringerLink
Log in

On factorization of the characteristic quasipolynomial of a system of linear differential equations with delay

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

We establish a factorization criterion for the characteristic quasipolynomial of a system of two linear autonomous differential equations with delay. On the base of this criterion we obtain several criteria of the asymptotic stability.

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. J. Hale Theory of Functional Differential Equations (Springer-Verlag, New York, 1977; Mir, Moscow, 1984).

    Book  MATH  Google Scholar 

  2. N. V. Azbelev and P. M. Simonov, Stability of Solutions of Ordinary Differential Equations (Permsk. Univ., Perm, 2001) [in Russian].

    Google Scholar 

  3. N. V. Azbelev and P. M. Simonov, Stability of Equations with Delay, Izv. Vyssh. Uchebn. Zaved. Mat., No. 6, 3–15 (1997) [RussianMathematics (Iz. VUZ) 41 (6), 1–14 (1997)].

    Google Scholar 

  4. N. V. Azbelev, V. P. Maksimov, and N. F. Rakhmatullina, Introduction to the Theory of Functional Differential Equations (Nauka, Moscow, 1991) [in Russian].

    MATH  Google Scholar 

  5. R. Bellman and K. L. Cooke Differential-Difference Equations (Acad. Press, New York, London, 1963; Mir, Moscow, 1967).

    MATH  Google Scholar 

  6. R. Horn and C. Johnson, Matrix Analysis (Cambridge University Press, New York, 1985; Mir, Moscow, 1989).

    Book  MATH  Google Scholar 

  7. Yu. A. Bakhturin, Basic Structures of Modern Algebra (Nauka, Moscow, 1990) [in Russian].

    MATH  Google Scholar 

  8. Yu. A. Alpin and N. A. Koreshkov, “On the Simultaneous Triangulability of Matrices,” Matem. Zametki 68(5), 648–652 (2000).

    Article  MathSciNet  Google Scholar 

  9. F. R. Gantmaher, The Theory of Matrices (AMS Chelsea Publ., 1958; Nauka, Moscow, 1967).

    Google Scholar 

  10. M. M. Postnikov, Stable Polynomials, 2nd Ed. (Editorial URSS, Moscow, 2004) [in Russian].

    Google Scholar 

  11. A. A. Andronov and A. T. Maier, “The Simplest Linear Systems with Retardation,” Avtomatika i Telemekhanika 7(2, 3), 95–106 (1946).

    MathSciNet  MATH  Google Scholar 

  12. A. I. Kir’yanen, Stability of Systems with Delay and Their Applications (S.-Peterburg Univ., St.-Petersburg, 1994) [in Russian].

    Google Scholar 

  13. T. Khokhlova, M. Kipnis, and V. Malygina, “The Stability Cone for a Delay Differential Matrix Equation,” Appl. Math. Lett. 24(5), 742–745 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  14. A. N. Bykova, “Investigation in the First Approximation of Stability of Systems of Two Nonlinear Differential Equations with Delay,” Candidate’s Dissertation in Mathematics and Physics (Cheboksary, 2002).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State National Research Polytechnical University of Perm, Komsomol’skii pr. 29, Perm, 614000, Russia

    M. V. Mulyukov

Authors
  1. M. V. Mulyukov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. V. Mulyukov.

Additional information

Original Russian Text © M.V. Mulyukov, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 9, pp. 38–44.

About this article

Cite this article

Mulyukov, M.V. On factorization of the characteristic quasipolynomial of a system of linear differential equations with delay. Russ Math. 57, 31–36 (2013). https://doi.org/10.3103/S1066369X13090053

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X13090053

Keywords and phrases

Search

Navigation