Domain of attraction of nonlinear discrete systems with delays
type: Item
instance of: scholarly article
title: Domain of attraction of nonlinear discrete systems with delays
zbMATH Open document ID: 0939.39013
DOI: 10.1016/S0898-1221(99)00222-9
author: Shuyong Li
author: Zhiling Pu
author: Qingyi Guo
author: Daoyi Xu
publication date: 2000-01-20T00:00:00Z
review text: The problem of determining the domain of attraction of nonlinear continuous or discrete systems with delays is rather complicated and still open. This paper presents one method for domain of attraction determination, which is applied to nonlinear discrete systems with bounded delays. Using the properties of nonnegative matrices and inequality techniques the author proves a new sufficient condition for the domain of attraction of a nonlinear discrete system with delays. The nonlinearity is assumed to be bounded by a ``quasi'' linear form. If the bound is linear, the domain of attraction becomes the entire state space. In this case, the condition is sufficient for the global exponential stability of the system. The domains of attraction of two numerical examples are given and it is known from simulation for fixed-delay that the system with initial function in the given domain of attraction is indeed exponential stable.
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 37G35
zbMATH DE Number: 1391646
zbMATH Keywords: domain of stability
zbMATH Keywords: domain of attraction
zbMATH Keywords: nonlinear discrete systems
zbMATH Keywords: nonlinear difference equations
zbMATH Keywords: bounded delay
zbMATH Keywords: global exponential stability
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1391646