New sufficient conditions for the stability of continuous and discrete time-delay interval systems
type: Item
instance of: scholarly article
title: New sufficient conditions for the stability of continuous and discrete time-delay interval systems
zbMATH Open document ID: 0868.34056
DOI: 10.1016/S0016-0032(96)00074-9
author: Chien-Hua Lee
author: Tsung-Lieh Hsien
published in: Journal of the Franklin Institute
publication date: 1997-05-28T00:00:00Z
review text: Stability for time-delay interval systems is investigated. Several new delay-independent sufficient conditions are given both for the continuous and the discrete case. The results are illustrated by some numerical examples. A typical continuous time delay system is \( \dot x(t)=Ax(t)+Bx(t-\tau) \) where \(x(\cdot)\in \mathbb{R}^n\) and \(\tau>0\). The interval property means that the matrices \(A\) and \(B\) satisfy: \[ A^-=[a_{ij}^-]\leq A=[a_{ij}]\leq A^+=[a_{ij}^+]\quad (i.e.\quad a_{ij}^-\leq a_{ij}\leq a_{ij}^+) \] \[ B^-=[b_{ij}^-]\leq B=[b_{ij}]\leq B^+=[b_{ij}^+]\quad (i.e.\quad b_{ij}^-\leq b_{ij}\leq b_{ij}^+) \] The stability is investigated by means of the roots of the characteristic equation \( \text{det}(sI-A-Be^{-s\tau})=0 \) and uses the so called Gerschgorin theorem. A typical result is the following one. The considered system is stable if the following condition holds: \[ \min\left\{ \max_i\sum_{j=1}^n(g_{ij}+f_{ij}), \max_i\sum_{j=1}^n(g_{ji}+f_{ji})\right\}<0 , \] with \(G=[g_{ij}]\), \(g_{ii}=a_{ii}^+\), \(g_{ij}=\max(|a_{ij}|,|a_{ij}^+|)\) for \(i\neq j\) and \(F=[f_{ij}]\), \(f_{ij}=\max(|b_{ij}|,|b_{ij}^+|)\).
reviewed by: Ivan Ginchev
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 93D09
zbMATH DE Number: 997657
zbMATH Keywords: time-delay interval systems
zbMATH Keywords: stability
zbMATH Keywords: characteristic equation
zbMATH Keywords: Gerschgorin theorem
MaRDI profile type: Publication
cites work: Near-decoupling of linear multivariable systems
cites work: Allowable coefficient perturbations with preserved stability of a Hurwitz polynomial†
cites work: A necessary and sufficient condition for the stability of interval matrices
cites work: Robust Schur-stability of control systems with interval plants
cites work: Stability analysis of interval matrices—continuous and discrete systems
cites work: Comments on ‘ A necessary and sufficient condition for the stability of interval matrices ’†
cites work: Sufficient condition for the positive definiteness of symmetric interval matrices
cites work: Sufficient condition for the asymptotic stability of interval matrices
cites work: Root-locus approach to the stability analysis of interval matrices
cites work: Stability analysis of dynamic interval systems
cites work: Stability analysis of interval matrices: improved bounds
cites work: Comments on ‘Stability of an entire polytope of polynomials’
cites work: Stability of interval parameter matrices
cites work: Necessary and sufficient conditions for stability of symmetric interval matrices
cites work: Stability margins of continuous time interval systems
cites work: Stability analysis of interval matrices: another sufficient condition
cites work: Inertia characteristics of self-adjoint matrix polynomials
cites work: A Discrete Dynamic Model with Distributed Transport Delays and Its Hierarchical Optimization for Preserving Stream Quality
cites work: Modelling and hierarchical optimization for oversaturated urban road traffic networks
cites work: Q3807934
cites work: Decentralized optimization for distributed-lag models of discrete systems
cites work: Q5661059
description: scientific article; zbMATH DE number 997657