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Automation and Remote Control

, Volume 72, Issue 1, pp 10–22 | Cite as

On the stabilization of a delayed system

  • B. G. Grebenshchikov
  • A. B. Lozhnikov
Determinate Systems

Abstract

Considered is the stabilization of systems of linear differential equations containing both constant and varying delays, the latter being unbounded. Stabilization methods for certain systems with constant coefficients are proposed.

Keywords

Remote Control Lyapunov Function Asymptotic Stability Stabilization Method Constant Delay 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bellman, R. and Cooke, K., Differential-Difference Equations, Santa Monica: Rand Corp., 1963. Translated under the title Differentsial’no-raznostnye uravneniya, Moscow: Mir, 1967.zbMATHGoogle Scholar
  2. 2.
    Halanay, A. and Wexler, D., Teoria calitativa a sistemelor cu impulsuri, Bucuresti: Academiei, 1968. Translated under the title Kachestvennaya teoriya impul’snykh sistem, Moscow: Mir, 1971.zbMATHGoogle Scholar
  3. 3.
    Mitropol’skii, Yu.A., Metod usredneniya v nelineinoi mekhanike (An Averaging Method in Nonlinear Mechanics), Kiev: Naukova Dumka, 1971.Google Scholar
  4. 4.
    Furasov, V.D., Ustoichivost’ i stabilizatsiya diskretnykh protsessov (Stability and Stabilization of Discrete-Time Processes), Moscow: Nauka, 1982.Google Scholar
  5. 5.
    Grebenshchikov, B.G. and Lozhnikov, A.B., Stabilization of a System with a Constant and a Linear Delay, Diff. Equat., 2004, vol. 40, no. 12, pp. 1587–1595.CrossRefMathSciNetGoogle Scholar
  6. 6.
    Krasovskii, N.N., On the Analytic Construction of Optimal Control in Systems with Time-lag, Prikl. Mat. Mekh., 1962, vol. 26, no. 1, pp. 39–51.MathSciNetGoogle Scholar
  7. 7.
    Markushin, E.M., Optimal’nye sistemy avtomaticheskogo regulirovaniya s zapazdyvaniem po vremeni (Optimal Automatic Regulation Systems with Time Delay), Saratov: Saratov. Univ., 1971.Google Scholar
  8. 8.
    Kim, A.V., Kwon, W.H., Pimenov, V.G., et al., Time-Delay System Toolbox (for Use with MATLAB). Beta Version, Korea, Seul: Seul Nat. Univ., 1998.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • B. G. Grebenshchikov
    • 1
  • A. B. Lozhnikov
    • 2
  1. 1.Ural Federal UniversityYekaterinburgRussia
  2. 2.Institute of Mathematics and Mechanics, Ural BranchRussian Academy of SciencesYekaterinburgRussia

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