A new delay-dependent criterion for neutral systems with multiple delays
type: Item
instance of: scholarly article
title: A new delay-dependent criterion for neutral systems with multiple delays
zbMATH Open document ID: 0995.34069
DOI: 10.1016/S0377-0427(00)00583-5
author: Ju H. Park
published in: Journal of Computational and Applied Mathematics
publication date: 2002-02-27T00:00:00Z
reviewed by: Manuel Calvo
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K40
Mathematics Subject Classification ID: 34K06
Mathematics Subject Classification ID: 34K25
zbMATH DE Number: 1669985
zbMATH Keywords: linear delay differential equations
zbMATH Keywords: neutral systems
zbMATH Keywords: stability of solutions
zbMATH Keywords: asymptotic stability
describes a project that uses: LMI toolbox
MaRDI profile type: Publication
cites work: Linear Matrix Inequalities in System and Control Theory
cites work: On the numerical integration of a symmetric system of difference- differential equations of neutral type
cites work: Q4003237
cites work: Stability in linear delay equations
cites work: Introduction to functional differential equations
cites work: Some simple criteria for stability of neutral delay-differential systems
cites work: Technical note Simple criteria for stability of neutral systems with multiple delays
cites work: Q3828361
cites work: Q4229393
cites work: The asymptotic stability of one-parameter methods for neutral differential equations
cites work: Stability of linear neutral delay-differential systems
review text: This paper is concerned with the asymptotic stability of neutral delay differential systems of the form NEWLINE\[NEWLINEx'(t)= A x(t) + \sum_{i=1}^m B_i x(t- h_i) + \sum_{i=1}^m C_i x'(t - h_i),NEWLINE\]NEWLINE where \( x(t)\) is the state vector, \( A, B_i, C_i \) are constant matrices and \( h_i\) are constant bounded delays. Further, \(A\) is assumed to be a Hurwitz matrix.NEWLINENEWLINENEWLINEIn this context, the author proves a theorem which provides a delay-dependent sufficient condition for the asymptotic stability. Since this sufficient condition depends on the existence of suitable constant matrices \( P, Q_i, X_i, Y_i, Z_i \) such that a big matrix \( \Sigma = \Sigma ( P, Q_i, X_i, Y_i, Z_i)\) depending on these matrices is negative definite, the proposed sufficient condition seems to be appropriate for checking the stability of low dimensional problems as shown for a two-dimensional system with two delays. Finally, as remarked by the author, the sufficient stability condition may be weaker than other similar sufficient conditions based on the logarithmic norm of \(A\).
description: scientific article; zbMATH DE number 1669985