On the coordinate synchronization problem for dynamical systems
type: Item
instance of: scholarly article
title: On the coordinate synchronization problem for dynamical systems
zbMATH Open document ID: 1076.34058
DOI: 10.1023/B:DIEQ.0000028709.33842.43
author: V. I. Vorotnikov
published in: Differential Equations
publication date: 2005-05-23T00:00:00Z
review text: The paper studies the coordinate synchronization problem for coupled dynamical systems. Particularly, there are studied two coupled systems with control \[ \dot x^i = X (t,x^1,x^2,u), \quad i=1,2, \] where \(x^i = (y^i,z^i)^T\) are phase vectors, \(\dim (y^1) = \dim (y^2)\), and \(u=u(t,x^1,x^2)\) is a control vector. The coordinate synchronization takes place when \(\| y^1(t,t_0,x_0^1,x_0^2) - y^2(t,t_0,x_0^1,x_0^2)\| \to 0\) as \(t\to \infty\) for some set of initial conditions \((x_0^1,x_0^2)\). Using the Lyapunov function method and ideas from the theory of partial stability, the author obtains sufficient conditions for coordinate synchronization.
reviewed by: S. Yanchuk
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 2170205
zbMATH Keywords: coordinate synchronization
zbMATH Keywords: Lyapunov function
zbMATH Keywords: partial stability
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2170205