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

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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

Full-text PDF (260 kB) Citations (43)

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Abstract: For the zero solution of the difference equation

x (n) = a x (n - m) + b x (n - k)

$x(n)=ax(n-m)+bx(n-k)$ with arbitrary delays

k, m

$k,m$ , the formulas of the stability domain boundaries were derived. For different

k

$k$ and

m

$m$ , 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:

G. Barrera, W. Barrera, J. P. Navarrete, “Egerváry's theorems for harmonic trinomials”, Acta Math. Hungar., 172:1 (2024), 170
P. S. Scherbakov, “Issledovanie effekta vspleska reshenii odnogo klassa raznostnykh uravnenii”, Avtomat. i telemekh., 2024, no. 6, 53–66
P. S. Shcherbakov, “Analysis of Peak Effects in the Solutions of a Class of Difference Equations”, ARC, 85:6 (2024), 587
P. S. Shcherbakov, “Analysis of Peak Effects in the Solutions of a Class of Difference Equations”, Autom Remote Control, 85:6 (2024), 512
A. S. Balandin, “Eksponentsialnaya ustoichivost avtonomnykh differentsialnykh uravnenii neitralnogo tipa. II”, Izv. vuzov. Matem., 2023, no. 4, 3–14
A. S. Balandin, “Exponential Stability of Autonomous Differential Equations of Neutral Type. II”, Russ Math., 67:4 (2023), 1
Gerardo Barrera, Waldemar Barrera, Juan Pablo Navarrete, “The Stability Region for Schur Stable Trinomials with General Complex Coefficients”, J Dyn Diff Equat, 2023
Waldemar Barrera, Julio Magaña, Juan Navarrete, “Trinomials, torus knots and chains”, Trans. Amer. Math. Soc., 2023
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
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
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
Pavel Shcherbakov, 2019 27th Mediterranean Conference on Control and Automation (MED), 2019, 618
Cermak J., Jansky J., Matsunaga H., “On Stability and Stabilization of Some Discrete Dynamical Systems”, Math. Meth. Appl. Sci., 41:10 (2018), 3684–3695
Bastinec J., Demchenko H., Diblik J., Khusainov D.Ya., “Exponential Stability of Linear Discrete Systems With Multiple Delays”, Discrete Dyn. Nat. Soc., 2018, 9703919
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
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
Polyak B.T., Shcherbakov P.S., Smirnov G., “Peak Effects in Stable Linear Difference Equations”, J. Differ. Equ. Appl., 24:9 (2018), 1488–1502
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
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
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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