Forced oscillations in control systems under near-resonance conditions
type: Item
instance of: scholarly article
title: Forced oscillations in control systems under near-resonance conditions
zbMATH Open document ID: 0932.93038
published in: Automation and Remote Control
publication date: 2000-02-03T00:00:00Z
review text: The author considers a single-loop control system whose dynamics is described by the differential equation \[ L(d/dt)x = M(d/dt)(f(x) + u(t)) \] where \(L(p)\) and \(M(p)\) are polynomials with constant coefficients, \(\deg L>\deg M \geq 0\), \(f(x)\) is a smooth function and the external action \(u(t)\) is assumed to be \(T\)-periodic. The resonance conditions under which \(L(p)\) has two primitive roots \(\lambda_{1,2} = \pm (2k \pi i)/T\) and the other roots lie left of the imaginary axis are assumed to be satisfied. The new method of multi-sheeted vector guiding functions developed by the author is applied to prove the existence of \(T\)-periodic trajectories for a given system.
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1290404
zbMATH Keywords: periodic solution
zbMATH Keywords: control system
zbMATH Keywords: forced oscillation
zbMATH Keywords: resonance condition
zbMATH Keywords: guiding function
zbMATH Keywords: multi-sheeted guiding function
zbMATH Keywords: dither
author: Dmitrii Rachinskii
reviewed by: Valerii V. Obukhovskij
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1290404