Mean square stability of difference equations with a stochastic delay
type: Item
instance of: scholarly article
title: Mean square stability of difference equations with a stochastic delay
zbMATH Open document ID: 1029.39005
DOI: 10.1016/S0362-546X(02)00133-5
author: T. L. Maizenberg
author: Jean-Pierre Richard
author: V. B. Kolmanovskii
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-11T00:00:00Z
review text: The subject of the paper is a nonlinear nonautonomous delay difference equation \[ x(n+1) = f(n,x(n),x(n-1),\dots, x(n-\eta(n+1)),\quad n\in \mathbb N. \] The function \(\eta: \mathbb N \to \{ 1,2,\dots,r \}\) counts the number of delays, it is subject to a discrete Markov process. Within this framework the authors prove two theorems on mean square asymptotic stability of the zero solution by applying Lyapunov stability methods. An elementary example illustrates the theory.
reviewed by: Stefan Hilger
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 60H25
zbMATH DE Number: 1879980
zbMATH Keywords: delay difference equations
zbMATH Keywords: Markov process
zbMATH Keywords: stochastic stability
zbMATH Keywords: stochastic delay
zbMATH Keywords: asymptotic stability
zbMATH Keywords: Lyapunov stability
MaRDI profile type: Publication
cites work: Stability of functional differential equations
cites work: Stability of linear feedback systems with random communication delays
cites work: Output feedback control under randomly varying distributed delays
full work available at URL: s0362-546x(02)00133-5
OpenAlex ID: W2066747764
description: scientific article; zbMATH DE number 1879980