Stability analysis for linear non-autonomous systems with continuously distributed multiple time-varying delays and applications
type: Item
instance of: scholarly article
title: Stability analysis for linear non-autonomous systems with continuously distributed multiple time-varying delays and applications
zbMATH Open document ID: 1238.34136
published in: Acta Mathematica Vietnamica
publication date: 2011-12-19T00:00:00Z
full work available at URL: Toc ACTA 2 36.htm
review text: New sufficient conditions for exponential stability of a nonautonomous linear system with distributed delays are given. The system has the form \[ \dot{x}(t)=A_0(t)x(t)+\sum_{i=1}^{p}A_i(t)x(t-h_i(t))+\sum_{k=1}^{q}D_k(t)\int_{t-r_k(t)}^t x(s)\,ds, \;\;t\geq0, \] where \(A_i\), \(D_k\) are given continuous matrix functions, the delay functions \(h_i\), \(r_k\) are bounded and \(dh_i/dt<1\), \(dr_k/dt<1\). The results are obtained by employing a Lyapunov-Krasovskii functional. Some conditions are presented in the form of Riccati inequalities. This gives the authors the opportunity to compute bounds that characterize the exponential stability rate of the solutions. To illustrate the usefulness of the new results, sufficient conditions for robust stability and stabilization of uncertain linear control system are obtained. Numerical examples are presented.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K06
Mathematics Subject Classification ID: 34K35
zbMATH DE Number: 5989458
zbMATH Keywords: exponential stability
zbMATH Keywords: stabilisation
zbMATH Keywords: Lyapunov-Krasovskii functional
zbMATH Keywords: Riccati equations
author: Trinh Tuan Anh
author: Le Van Hien
author: V. N. Phat
reviewed by: Oleg Anashkin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5989458