Separation of motions in multirate discontinuous systems with time delay
type: Item
instance of: scholarly article
title: Separation of motions in multirate discontinuous systems with time delay
zbMATH Open document ID: 0932.93040
published in: Automation and Remote Control
publication date: 1999-06-29T00:00:00Z
review text: The author considers a system of the form \[ \mu dz/dt = g(z,s,x,u), \quad ds/dt = h_1(z,s,x,u), \quad dx/dt = h_2(z,s,x,u) \] where \(z \in R^m\), \(s \in R\), \(x \in R^n\), \(u(s) = - \text{sign}[s(t-1)]\), \(g\),\(h_1\) and \(h_2\) are smooth functions and \(\mu\) is a small parameter. Sufficient conditions are given under which for sufficiently small \(\mu\) there exists an orbitally asymptotically stable periodic solution. The algorithm of the construction of an asymptotics of a periodic solution is suggested. An example illustrating how the obtained results can be used for the separation of motions in singularly perturbed discontinuous systems with delay is given.
Mathematics Subject Classification ID: 93C23
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34D15
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93D15
zbMATH DE Number: 1263174
zbMATH Keywords: periodic solution
zbMATH Keywords: singularly perturbed system
zbMATH Keywords: small parameter
zbMATH Keywords: stability
zbMATH Keywords: time delay
zbMATH Keywords: discontinuous system
zbMATH Keywords: dither
zbMATH Keywords: separation of motions
author: Leonid M. Fridman
reviewed by: Valerii V. Obukhovskij
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1263174