Exponential and global stability of nonlinear dynamical systems relative to initial time difference
type: Item
instance of: scholarly article
title: Exponential and global stability of nonlinear dynamical systems relative to initial time difference
zbMATH Open document ID: 1216.37010
author: An Li
author: Wei Lv
author: Jianxiong Ye
published in: Applied Mathematics and Computation
publication date: 2011-03-08T00:00:00Z
review text: The authors investigate the stability of solutions of a nonautonomous system \(\dot x = f(t, x)\) of nonlinear ordinary differential equations for \(f \in C({\mathbb R}_+ \times {\mathbb R}^n, {\mathbb R}^n)\) with respect to a difference in the initial times. To do so they develop a comparison principle for solutions with different starting times using Lyapunov functions \(V \in C({\mathbb R}_+ \times {\mathbb R}^n, {\mathbb R_+^m})\) that are locally Lipschitz in the space variable \(x\). Sufficient conditions for stability are derived. The theory is illustrated with an example for which \(x \in {\mathbb R}^2\).
reviewed by: Douglas S. Shafer
Mathematics Subject Classification ID: 37C60
Mathematics Subject Classification ID: 34A12
zbMATH DE Number: 5862531
zbMATH Keywords: exponential stability
zbMATH Keywords: global stability
zbMATH Keywords: comparison principle
zbMATH Keywords: vector Lyapunov function
MaRDI profile type: Publication
full work available at URL: j.amc.2010.12.097
OpenAlex ID: W2072692511
cites work: Differential Inequalities with Initial Time Difference
cites work: Integro-differential inequalities with initial time difference and applications
cites work: Delay integro-differential inequalities with initial time difference and applications
cites work: Another approach to the theory of differential inequalities realtive to changes in the initial times
cites work: Q3995013
cites work: Differential inequalities with initial time difference and applications
cites work: Stability and boundedness criteria for nonlinear differential systems relative to initial time difference and applications
cites work: Impulsive optimal control model for the trajectory of horizontal wells
cites work: Stochastic optimal control and algorithm of the trajectory of horizontal wells
cites work: Stability and optimal control of microorganisms in continuous culture
cites work: Perturbing Lyapunov functions and stability criteria for initial time difference.
cites work: Practical stability of nonlinear differential equation with initial time difference
cites work: Variation of parameters formulae with initial time difference for linear integrodifferential equations
DOI: 10.1016/J.AMC.2010.12.097
description: scientific article; zbMATH DE number 5862531