Control of the spectrum of irregular oscillations of linear systems with coinciding ranks of the matrix multiplying the control and the extended matrix
type: Item
instance of: scholarly article
title: Control of the spectrum of irregular oscillations of linear systems with coinciding ranks of the matrix multiplying the control and the extended matrix
zbMATH Open document ID: 1242.34117
DOI: 10.1134/S0012266111090035
author: A. K. Demenchuk
published in: Differential Equations
publication date: 2012-01-18T00:00:00Z
review text: Periodic, linear, continuous-time, finite-dimensional control systems with time dependent coefficients are considered. It is assumed that the control is defined in the form of a linear feedback with respect to the state variables, and is periodic with the same period as the system itself. The main purpose is to synthesize this feedback in order to control the spectrum of irregular oscillations. A necessary and sufficient condition for the solution of this problem is formulated and proved. The main requirement is to satisfy certain rank condition. Finally, some remarks and comments on the properties of the spectrum of irregular oscillations are presented. Similar problems have been considered in the paper [\textit{P. Brunovski}, Controllability and linear closed-loop controls in linear periodic systems. J. Differ. Equations, 600, No. 3, 296--313 (1969; Zbl 0176.06301)].
reviewed by: Jerzy Klamka
Mathematics Subject Classification ID: 34H05
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93B52
zbMATH DE Number: 5998571
zbMATH Keywords: linear control systems
zbMATH Keywords: periodic control systems
zbMATH Keywords: frequency oscillation
MaRDI profile type: Publication
cites work: Controllability and linear closed-loop controls in linear periodic systems
cites work: The problem of the control of the spectrum of strongly irregular periodic oscillations
cites work: Q3027440
cites work: Partially irregular almost-periodic solutions to ordinary differential systems
description: scientific article; zbMATH DE number 5998571