Delay-dependent exponential stability criteria for nonlinear time-varying discrete systems with multiple time delays
type: Item
instance of: scholarly article
title: Delay-dependent exponential stability criteria for nonlinear time-varying discrete systems with multiple time delays
zbMATH Open document ID: 0893.93023
DOI: 10.1016/S0016-0032(96)00061-0
author: Yeong-Jeu Sun
author: Gwo-Jeng Yu
published in: Journal of the Franklin Institute
publication date: 1998-08-24T00:00:00Z
review text: The following nonlinear discrete time-delay system is considered: \[ x(n+1)= \sum^p_{i= 1}A_i(x,1\dots p)x(n- h_i), \] \[ x(n)= \phi(n),\quad -h_p\leq n\leq 0 \] \((0\leq h_1< h_2<\cdots< h_p)\). It is assumed that the nonlinearity \(A\) is bounded by \[ \| A_i(.,.)\|\leq b_i(n),\quad\forall i,n. \] Then if there exists \(J\) and \(0<r<1\) such that \[ \sum^p_{i=1} {1\over r^{1+ h_i}} b_i(n+ J+ h_i)< 1,\quad\forall n>0 \] it is shown that the equation is stable with decay rate at least \(r\). A simple example is given.
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 1028993
zbMATH Keywords: stability
zbMATH Keywords: nonlinear discrete time-delay system
reviewed by: S. P. Banks
MaRDI profile type: Publication
cites work: Q4079440
cites work: Discrete systems. Analysis, control and optimization
cites work: Delay-independent stability criteria for discrete-delay systems
cites work: Simple stability criteria for nonlinear time-varying discrete systems
cites work: Delay-independent exponential stability criteria for time-varying discrete delay systems
description: scientific article; zbMATH DE number 1028993