On delay-dependent global asymptotic stability for pendulum-like systems
type: Item
instance of: scholarly article
title: On delay-dependent global asymptotic stability for pendulum-like systems
zbMATH Open document ID: 1188.34098
published in: Journal of Optimization Theory and Applications
publication date: 2009-11-27T00:00:00Z
review text: This paper deals with global asymptotic stability of the trivial solution of the delayed nonlinear pendulum-like system \[ x'(t) = Px(t) + P_hx(t-h) + R\varphi(S^Tx(t)), \] where \(h>0\) is a given constant, \(P, P_h, R\) and \(S\) are real constant matrices of dimensions \((n+1)\times(n+1)\), \((n+1)\times(n+1)\), \((n+1)\times m\) and \((n+1)\times m\) respectively, and the mapping \(\varphi\) satisfies \(\varphi_i(\sigma) = \varphi_i(\sigma_i)\) with \(\sigma = (\sigma_1, \sigma_2, \dots, \sigma_m)\). With an appropriate linear transformation, the above system can be written in a canonical form. Then global asymptotic stability and robust global asymptotic stability are obtained under the requirement of existence of a positive number and some (at least 12) matrices satisfying certain matrix inequalities.
reviewed by: Zhanyuan Hou
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 5640249
zbMATH Keywords: pendulum-like systems
zbMATH Keywords: delayed system
zbMATH Keywords: global asymptotic stability
author: Pingli Lu
author: Ying Yang
describes a project that uses: LMI toolbox
MaRDI profile type: Publication
full work available at URL: s10957-009-9578-4
OpenAlex ID: W2133820715
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DOI: 10.1007/S10957-009-9578-4
description: scientific article; zbMATH DE number 5640249