Moscow University Mathematics Bulletin

, Volume 74, Issue 3, pp 121–126 | Cite as

Reducibility of Linear Differential Systems to Linear Differential Equations

  • I. N. SergeevEmail author


Lyapunov reducibility of any bounded and sometimes unbounded linear homogeneous differential system to some bounded linear homogeneous differential equation is established. The preservation of the additional property of periodicity of coefficients is guaranteed, and for two-dimensional or complex systems the constancy of their coefficients is preserved. The differences in feasibility of asymptotic and generalized Lyapunov reducibility from Lyapunov one are indicated.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The author is grateful to V. V. Bykov for valuable remarks contributed to significant improvement in the text of the paper.


  1. 1.
    V. A. Zaitsev, “Global Attainability and Global Lyapunov Reducibility of Two- and Three-Dimensional Linear Control Systems with Constant Coefficients,” Vestn. Udmurt. Univ., Matem. 1, 31 (2003).Google Scholar
  2. 2.
    I. N. Sergeev, “Limit Values of Lyapunov Exponents of Linear Equations,” Differ. Uravn., 46 (11), 1664 (2010).Google Scholar
  3. 3.
    B. P. Demidovich, Lectures in Mathematical Theory of Stability (Nauka, Moscow, 1967) [in Russian].zbMATHGoogle Scholar
  4. 4.
    I. N. Sergeev, “Control of Solutions to a Linear Differential Equation,” Vestnik Mosk. Univ., Matem. Mekhan., No. 3, 25 (2009).Google Scholar
  5. 5.
    I. N. Sergeev, “Oscillation, Rotatability, and Wandering Characteristic Indicators for Differential Systems Determining Rotations of Plane,” Vestnik Mosk. Univ., Matem. Mekhan., No. 1, 21 (2019).Google Scholar
  6. 6.
    B. F. Bylov, R. E. Vinograd, D. M. Grobman, and V. V. Nemytskii, Theory of Lyapunov Exponents and its Application to Stability Issues (Nauka, Moscow, 1966) [in Russian].zbMATHGoogle Scholar
  7. 7.
    V. P. Basov, “Structure of Solutions in a Right Differential System,” Vestnik Leningr. Univ., No. 12, 3 (1952).Google Scholar
  8. 8.
    Yu. S. Bogdanov, “To the Theory of Linear Differential Equations,” Doklady Akad. Nauk SSSR 104 (6), 813 (1955).MathSciNetGoogle Scholar
  9. 9.
    D. M. Grobman, “Characteristic Indicators of Systems Close to Linear Ones,” Matem. Sbornik 30(72) (1), 121 (1952).MathSciNetGoogle Scholar

Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityLeninskie Gory, MoscowRussia

Personalised recommendations