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Automation and Remote Control

, Volume 65, Issue 11, pp 1710–1723 | Cite as

Stability of the Trinomial Linear Difference Equations with Two Delays

  • M. M. Kipnis
  • R. M. Nigmatullin
Article

Abstract

For the zero solution of the difference equation x(n) = ax(n - m) + bx(n - k) with arbitrary delays k, m, the formulas of the stability domain boundaries were derived. For different k and m, the stability domains were compared in the quadrants of the plane (a, b).

Keywords

Mechanical Engineer System Theory Domain Boundary Difference Equation Stability Domain 
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.
    Nikolaev, Yu.P., On Symmetry and Other Properties of the Multidimensional Asymptotic Stability of the Linear Discrete Systems, Avtom. Telemekh., 2001, no. 4, pp. 98–108.Google Scholar
  2. 2.
    Nikolaev, Yu.P., On Studying the Geometry of the Set of the Stable Polynomials of the Linear Discrete Systems, Avtom. Telemekh., 2002, no. 7, pp. 44–54.Google Scholar
  3. 3.
    Levin, S.A. and May, R., A Note on Difference-delay Equations, Theor. Pop. Biol., 1976, vol. 9, pp. 178–187.Google Scholar
  4. 4.
    Rodionov, A.M., Some Modifications of the Theorems of the Second Lyapunov Method for Discrete Equations, Avtom. Telemekh., 1992, no. 9, pp. 86–93.Google Scholar
  5. 5.
    Kolmanovskii, V.B., On Applying the Second Lyapunov Method to the Difference Volterra Equations, Avtom. Telemekh., 1995, no. 11, pp. 50–64.Google Scholar
  6. 6.
    Kuruklis, S.A., The Asymptotic Stability of x(n + 1) − ax(n) +bx(n − k) = 0, J. Math. Anal. Appl., 1994, vol. 188, pp. 719–731.Google Scholar
  7. 7.
    Dannan, F.M. and Elaydi, S.N., Asymptotic Stability of Linear Difference Equations of Advanced Type, Technical Report no. 60, 2001, pp. 1–15(htpp://www.trinity.edu/departments/mathematics).Google Scholar
  8. 8.
    Kipnis, M.M. and Nigmatullin, R.M., Stability of Some Difference Equations with Two Delays, Avtom.Telemekh., 2003, no. 5, pp. 122–130.Google Scholar
  9. 9.
    Cohn, A., Uber die Anzahl der Wurzeln einer algebraishen Gleichung in einem Kreise, Math. Zeitschrift, 1922, vol. 14, pp. 110–148.Google Scholar
  10. 10.
    Kozak, A.D. and Novoselov, A.N., Asymptotic Behavior of the Solutions of the Linear Uniform Difference Equation of the Second Order, Mat. Zametki, 1999, vol. 66, no. 2, pp. 211–215.Google Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2004

Authors and Affiliations

  • M. M. Kipnis
    • 1
  • R. M. Nigmatullin
    • 1
  1. 1.Chelyabinsk State Pedagogical UniversityChelyabinskRussia

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