Modal control of systems with delay
type: Item
instance of: scholarly article
zbMATH Open document ID: 0974.49014
author: A. T. Kozhamentov
author: N. V. Kosarevskaya
author: Denis Khusainov
publication date: 2001-09-16T00:00:00Z
Mathematics Subject Classification ID: 49K25
zbMATH DE Number: 1646397
zbMATH Keywords: modal control
zbMATH Keywords: systems with delay
zbMATH Keywords: closed system
zbMATH Keywords: characteristic equation
zbMATH Keywords: necessary and sufficient conditions
MaRDI profile type: Publication
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title: Modal control of systems with delay
published in: Zhurnal Obchyslyuval'noïta Prykladnoï Matematyky
review text: The authors consider a system of differential equations with delay NEWLINE\[NEWLINE\dot x(t)=Ax(t)+A_1x(t-\tau)+bu(t),NEWLINE\]NEWLINE where \(A=\{a_{ij}\}\), \(A_1= \{a_{ij}^1\}\), \(i,j=1,\ldots,n,\;b\in R^{n}\). The problem of modal control for the considered system is the following. Find a control in the form \(u(t)=\sum_{j=0}^{m}c_{j}^{T}x(t-j\tau)\), \(c_{j}^{T}= (c_{1j},\ldots, c_{nj})\), such that the characteristic equation of the closed system NEWLINE\[NEWLINE\dot x(t)=Ax(t)+A_1x(t-\tau)+b\sum_{j=0}^{m} c_{j}^{T}x(t-j\tau)NEWLINE\]NEWLINE has a given form \(\lambda^{n}+q_1(\lambda) \lambda^{n-1}+\ldots+q_{n}(\lambda)=0\), \(q_{i}=\sum_{j=0}^{i} e^{-i\lambda\tau}q_{ij}, q_{00}=1\). The necessary and sufficient conditions of modal controllability of the considered system are obtained.
reviewed by: Aleksandr D. Borisenko
description: scientific article; zbMATH DE number 1646397