D. G. Korenevskij, “Stability Criteria for Solutions of Systems of Linear Deterministic or Stochastic Delay Difference Equations with Continuous Time”, Mat. Zametki, 70:2 (2001), 213–229; Math. Notes, 70:2 (2001), 192

Matematicheskie Zametki

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Forthcoming papers
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Mat. Zametki:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Matematicheskie Zametki, 2001, Volume 70, Issue 2, Pages 213–229
DOI: https://doi.org/10.4213/mzm735 (Mi mzm735)

This article is cited in 17 scientific papers (total in 17 papers)

Stability Criteria for Solutions of Systems of Linear Deterministic or Stochastic Delay Difference Equations with Continuous Time

D. G. Korenevskij

Institute of Mathematics, Ukrainian National Academy of Sciences

Full-text PDF (230 kB) Citations (17)

References:

PDF

HTML

DOI: https://doi.org/10.4213/mzm735

Abstract: We give spectral and algebraic coefficient criteria (necessary and sufficient conditions) as well as sufficient algebraic coefficient conditions for the Lyapunov asymptotic stability of solutions to systems of linear deterministic or stochastic delay difference equations with continuous time under white noise coefficient perturbations for the case in which all delay ratios are rational. For stochastic systems, mean-square asymptotic stability is studied. The Lyapunov function method is used. Our criteria on algebraic coefficients and our sufficient conditions are stated in terms of matrix Lyapunov equations (for deterministic systems) and matrix Sylvester equations (for stochastic systems).

Received: 22.02.2001

English version:
Mathematical Notes, 2001, Volume 70, Issue 2, Pages 192–205
DOI: https://doi.org/10.1023/A:1010202824752

Bibliographic databases:

UDC: 517.929+519.248

Language: Russian

Citation: D. G. Korenevskij, “Stability Criteria for Solutions of Systems of Linear Deterministic or Stochastic Delay Difference Equations with Continuous Time”, Mat. Zametki, 70:2 (2001), 213–229; Math. Notes, 70:2 (2001), 192–205

Citation in format AMSBIB

\Bibitem{Kor01}

\by D.~G.~Korenevskij

\paper Stability Criteria for Solutions of Systems of Linear Deterministic or Stochastic Delay Difference Equations with Continuous Time

\jour Mat. Zametki

\yr 2001

\vol 70

\issue 2

\pages 213--229

\mathnet{http://mi.mathnet.ru/mzm735}

\crossref{https://doi.org/10.4213/mzm735}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1882411}

\zmath{https://zbmath.org/?q=an:1022.39003}

\transl

\jour Math. Notes

\yr 2001

\vol 70

\issue 2

\pages 192--205

\crossref{https://doi.org/10.1023/A:1010202824752}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000171684100024}

Linking options:

https://www.mathnet.ru/eng/mzm735

https://doi.org/10.4213/mzm735

https://www.mathnet.ru/eng/mzm/v70/i2/p213

This publication is cited in the following 17 articles:

Leonid Shaikhet, “Unsolved problem about stability of stochastic difference equations with continuous time and distributed delay”, Modern Stochastics: Theory and Applications, 2024, 1
Peics H., Roznjik A., Krekic V.P., Takacs M., “System of delay difference equations with continuous time with lag function between two known functions”, The 10'th Colloquium on the Qualitative Theory of Differential Equations (Szeged, Hungary), 2016, 18
Li G., Chen M., “The Stability and Stabilization of Stochastic Delay-Time Systems”, Math. Probl. Eng., 2014, 272745
Shaikhet L., “About an Unsolved Stability Problem for a Stochastic Difference Equation with Continuous Time”, J. Differ. Equ. Appl., 17:3 (2011), 441–444
Leonid Shaikhet, Lyapunov Functionals and Stability of Stochastic Difference Equations, 2011, 227
S. M. Dobrovol'skii, T. M. Strugova, “The method of parametric Lyapunov functions for Markov dynamic systems”, J. Appl. Ind. Math., 2:1 (2008), 39
Luo, JW, “Stability in probability of nonlinear stochastic Volterra difference equations with continuous variable”, Stochastic Analysis and Applications, 25:6 (2007), 1151
Paternoster, B, “Mean square summability of solution of Stochastic difference second-kind volterra equation with small nonlinearity”, Advances in Difference Equations, 2007, 65012
Beatrice Paternoster, Leonid Shaikhet, “Mean Square Summability of Solution of Stochastic Difference Second-Kind Volterra Equation with Small Nonlinearity”, Adv. Differ Equ., 2007 (2007), 1
Shaikhet, L, “About stability of a difference analogue of a nonlinear integro-differential equation of convolution type”, Applied Mathematics Letters, 19:11 (2006), 1216
Shaikhet, L, “Some new aspect of Lyapunov type theorems for stochastic difference equations with continuous time”, Asian Journal of Control, 8:1 (2006), 76
Makiko Hotta, Tohru Hasegawa, Kazushi Ohishi, Munetaka Hosokawa, Hiroshi Hara, Toshihiro Kato, “Effects of elimination of Chrysanthemum stunt viroid from infected plants on growth and flowering of chrysanthemum cv. “Jinba””, Ann. Rept. Kansai Pl. Prot., 48 (2006), 39
T. M. Strugova, “On the Stability of Linear Stochastic Finite-Difference Systems with Almost-Periodic Coefficients”, Math. Notes, 78:3 (2005), 432–436
S. M. Dobrovolskii, T. M. Strugova, “The method of parametric Lyapunov functions for Markov dynamical systems”, J. Appl. Industr. Math., 2:1 (2008), 39–45
Shaikhet, L, “General method of Lyapunov functionals construction in stability investigations of nonlinear stochastic difference equations with continuous time”, Stochastics and Dynamics, 5:2 (2005), 175
Shiro Fukuta, Yoshihisa Nimi, Kazushi Ohishi, Yukie Yoshimura, Naoko Anai, Makiko Hotta, Masahiro Fukaya, Toshihiro Kato, Toshio Oya, Michio Kanbe, “Development of reverse transcription loop-mediated isothermal amplification (RT-LAMP) method for detection of two viruses and chrysanthemum stunt viroid”, Ann. Rept. Kansai Pl. Prot., 47 (2005), 31
Shaikhet, LE, “Construction of Lyapunov functionals for stochastic difference equations with continuous time”, Mathematics and Computers in Simulation, 66:6 (2004), 509

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

Statistics & downloads:
Abstract page:	750
Full-text PDF :	272
References:	78
First page:	1

Registration to the website

Logotypes