On spectral controllability of multi-input time-delay systems
type: Item
instance of: scholarly article
title: On spectral controllability of multi-input time-delay systems
zbMATH Open document ID: 0614.93009
DOI: 10.1016/0167-6911(85)90041-6
published in: Systems \& Control Letters
publication date: 1985-01-01T00:00:00Z
review text: The systems under consideration are of the form \(\dot x(t)=A_ 0x(t)+A_ 1x(t-h)+...+A_ Nx(t-Nh)+Bu(t)\) where x(t) is in \(R^ n\) and u(t) in \(R^ m\). The spectral controllability condition, as is well- known, can be expressed as rank(sI-\(\sum^{N}_{k=0}(\exp -skh)A_ k,B)=n\) for all complex s. The question considered is under what assumption B can be substituted by Br, for some vector r, without violating this condition. For systems without delays \((N=0)\) the situation is clear: \(A_ 0\) must be cyclic. For time-delay systems the main theorem in the paper gives the following necessary and sufficient conditions for the existence of a vector r with the required properties: 1) A(z) is cyclic for some complex z, where A(z) is defined as \(A(z)=A_ 0+zA_ 1+...+z^ NA_ N.\) 2) If s is such that \(A(e^{-sh})\) is not cyclic then rank \([sI-A(e^{- sh})]\geq n-1\).
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 34K35
Mathematics Subject Classification ID: 93C35
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 93B03
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 3995518
zbMATH Keywords: spectral controllability condition
zbMATH Keywords: time-delay systems
author: Andrzej Manitius
author: Vasilios I. Manousiouthakis
MaRDI profile type: Publication
full work available at URL: 0167-6911(85)90041-6
OpenAlex ID: W2081388591
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description: scientific article; zbMATH DE number 3995518