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Avtomatika i Telemekhanika, 2004, Issue 11, Pages 25–39 (Mi at1657)  

This article is cited in 43 scientific papers (total in 43 papers)

Deterministic Systems

Stability of the trinomial linear difference equations with two delays

M. M. Kipnis, R. M. Nigmatulin

Chelyabinsk State Pedagogical University
References:
Abstract: For the zero solution of the difference equation x(n)=ax(nm)+bx(nk)x(n)=ax(nm)+bx(nk) with arbitrary delays k,mk,m, the formulas of the stability domain boundaries were derived. For different kk and mm, the stability domains were compared in the quadrants of the plane (a,b)(a,b).
Presented by the member of Editorial Board: B. T. Polyak

Received: 30.12.2002
English version:
Automation and Remote Control, 2004, Volume 65, Issue 11, Pages 1710–1723
DOI: https://doi.org/10.1023/B:AURC.0000047886.46498.79
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. M. Kipnis, R. M. Nigmatulin, “Stability of the trinomial linear difference equations with two delays”, Avtomat. i Telemekh., 2004, no. 11, 25–39; Autom. Remote Control, 65:11 (2004), 1710–1723
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/at1657
  • https://www.mathnet.ru/eng/at/y2004/i11/p25
  • This publication is cited in the following 43 articles:
    1. G. Barrera, W. Barrera, J. P. Navarrete, “Egerváry's theorems for harmonic trinomials”, Acta Math. Hungar., 172:1 (2024), 170  crossref
    2. P. S. Scherbakov, “Issledovanie effekta vspleska reshenii odnogo klassa raznostnykh uravnenii”, Avtomat. i telemekh., 2024, no. 6, 53–66  mathnet  crossref
    3. P. S. Shcherbakov, “Analysis of Peak Effects in the Solutions of a Class of Difference Equations”, ARC, 85:6 (2024), 587  crossref
    4. P. S. Shcherbakov, “Analysis of Peak Effects in the Solutions of a Class of Difference Equations”, Autom Remote Control, 85:6 (2024), 512  crossref
    5. A. S. Balandin, “Eksponentsialnaya ustoichivost avtonomnykh differentsialnykh uravnenii neitralnogo tipa. II”, Izv. vuzov. Matem., 2023, no. 4, 3–14  mathnet  crossref
    6. A. S. Balandin, “Exponential Stability of Autonomous Differential Equations of Neutral Type. II”, Russ Math., 67:4 (2023), 1  crossref
    7. Gerardo Barrera, Waldemar Barrera, Juan Pablo Navarrete, “The Stability Region for Schur Stable Trinomials with General Complex Coefficients”, J Dyn Diff Equat, 2023  crossref
    8. Waldemar Barrera, Julio Magaña, Juan Navarrete, “Trinomials, torus knots and chains”, Trans. Amer. Math. Soc., 2023  crossref
    9. Tomasek P., “Stability and Instability Regions For a Three Term Difference Equation”, Difference Equations and Discrete Dynamical Systems With Applications, Icdea 2018, Springer Proceedings in Mathematics & Statistics, 312, eds. Bohner M., Siegmund S., Hilscher R., Stehlik P., Springer International Publishing Ag, 2020, 355–364  crossref  isi
    10. Shcherbakov P., “The Trinomial Equation Xk+1 - Ax(K) + Bx(K-N)=0: Analysis of the Nonasymptotic Behavior of Solutions”, 2019 27Th Mediterranean Conference on Control and Automation (Med), Mediterranean Conference on Control and Automation, IEEE, 2019, 618–623  isi
    11. Diblik J., Ruzickova M., Vazanova G., “Exponential-Type Estimates of Solutions Linear Discrete Systems With Constant Coefficients and Single Delay”, AIP Conference Proceedings, 2116, eds. Simos T., Tsitouras C., Amer Inst Physics, 2019, 310002  crossref  isi  scopus
    12. Pavel Shcherbakov, 2019 27th Mediterranean Conference on Control and Automation (MED), 2019, 618  crossref
    13. Cermak J., Jansky J., Matsunaga H., “On Stability and Stabilization of Some Discrete Dynamical Systems”, Math. Meth. Appl. Sci., 41:10 (2018), 3684–3695  crossref  isi  scopus
    14. Bastinec J., Demchenko H., Diblik J., Khusainov D.Ya., “Exponential Stability of Linear Discrete Systems With Multiple Delays”, Discrete Dyn. Nat. Soc., 2018, 9703919  crossref  mathscinet  isi  scopus
    15. Bastinec J., Diblik J., Khusainov D., “Stability of Linear Discrete Systems With Variable Delays”, AIP Conference Proceedings, 1978, Amer Inst Physics, 2018, UNSP 430005-1  crossref  isi  scopus
    16. Diblik J., Khusainov D.Ya., Ruzickova M., “Exponential Stability of Linear Discrete Systems With Delay”, AIP Conference Proceedings, 1978, Amer Inst Physics, 2018, UNSP 430004-1  crossref  isi  scopus
    17. Polyak B.T., Shcherbakov P.S., Smirnov G., “Peak Effects in Stable Linear Difference Equations”, J. Differ. Equ. Appl., 24:9 (2018), 1488–1502  crossref  mathscinet  zmath  isi  scopus
    18. A. A. Kandakov, K. M. Chudinov, “Effektivnye kriterii eksponentsialnoi ustoichivosti avtonomnykh raznostnykh uravnenii”, Vestnik Tambovskogo universiteta. Seriya: estestvennye i tekhnicheskie nauki, 23:123 (2018), 402–414  mathnet  crossref  elib
    19. Tomasek P., “Visualization and Analysis of Stability Regions of Certain Discretization of Differential Equation With Constant Delay”, Mem. Differ. Equ. Math. Phys., 72 (2017), 131–139  mathscinet  zmath  isi
    20. Diblik J., “Exponential Stability of Linear Discrete Systems With Nonconstant Matrices and Nonconstant Delay”, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2016 (ICNAAM-2016), AIP Conference Proceedings, 1863, eds. Simos T., Tsitouras C., Amer Inst Physics, 2017, UNSP 480003-1  crossref  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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