On the asymptotical behaviour of solutions of a class of nonlinear control systems
type: Item
instance of: scholarly article
title: On the asymptotical behaviour of solutions of a class of nonlinear control systems
zbMATH Open document ID: 0965.93091
DOI: 10.1007/BF02459175
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 2000-09-04T00:00:00Z
review text: The author is interested in the asymptotic behavior of solutions to a nonlinear system of the form \[ \dot x= Ax+ B\phi(\sigma),\quad \sigma= C^Tx, \] where \(\phi\) is a continuous function satisfying certain sector conditions. The system is said to be dichotomous if any bounded solution is attracted by the set of equilibrium points \(D\), and globally asymptotic if every solution is attracted by \(D\). On the basis of a LaSalle's invariance principle of integral type, the author gives some sufficient conditions for dichotomy and for global asymptotic behavior.
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 1502188
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: nonlinear system
zbMATH Keywords: invariance principle
zbMATH Keywords: dichotomy
zbMATH Keywords: global asymptotic behavior
author: Zhidong Teng
reviewed by: Andrea Bacciotti
MaRDI profile type: Publication
cites work: Q3335637
cites work: Q4881154
cites work: Absolute stability of a control system with several nonlinear stationary elements in the case of an infinite sector
cites work: Absolute stability of control systems with several nonlinear stationary elements
cites work: Q3974326
cites work: Necessary and sufficient criteria for absolute stability of the direct control system
cites work: Q4698808
cites work: Q3360094
cites work: Stability theory for ordinary differential equations
description: scientific article; zbMATH DE number 1502188