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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, Volume 30, Issue 2, Pages 290–311
DOI: https://doi.org/10.35634/vm200211
(Mi vuu726)
 

This article is cited in 4 scientific papers (total in 4 papers)

MATHEMATICS

On a linear autonomous descriptor equation with discrete time. I. Application to the $0$-controllability problem

V. E. Khartovskii

Yanka Kupala State University of Grodno, ul. Ozheshko, 22, Grodno, 230023, Belarus
Full-text PDF (323 kB) Citations (4)
References:
Abstract: We consider a linear homogeneous autonomous descriptor equation with discrete time
$$B_0g(k+1)+\sum_{i=1}^mB_ig(k+1-i)=0,\quad k=m,m+1,\ldots,$$
with rectangular (in general case) matrices $B_i$. Such an equation arises in the study of the most important control problems for systems with many commensurate delays in control: the 0-controllability problem, the synthesis problem of the feedback-type regulator, which provides calming to the solution of the original system, the modal controllability problem (controllability of the coefficients of characteristic quasipolynomial), the spectral reduction problem and the problem of observers' synthesis for a dual surveillance system. For the studied descriptor equation with discrete time, a subspace of initial conditions for which this equation is solvable is described based on the solution of a finite chain of homogeneous algebraic systems. The representation of all its solutions is obtained in the form of some explicit recurrent formula convenient for the organization of the computational process. Some properties of this equation that are used in the problems of regulator synthesis for continuous systems with many commensurate delays in control are studied. A distinctive feature of the presented study of the object under consideration is the use of an approach that does not require the construction of transformations reducing the matrices of the original equation to different canonical forms.
Keywords: linear systems with multiple delays, linear descriptor autonomous equation with discrete time, subspace of initial conditions, representation of the solution.
Received: 22.04.2020
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: 93B99, 93C55
Language: Russian
Citation: V. E. Khartovskii, “On a linear autonomous descriptor equation with discrete time. I. Application to the $0$-controllability problem”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:2 (2020), 290–311
Citation in format AMSBIB
\Bibitem{Kha20}
\by V.~E.~Khartovskii
\paper On a linear autonomous descriptor equation with discrete time. I.~Application to the $0$-controllability problem
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2020
\vol 30
\issue 2
\pages 290--311
\mathnet{http://mi.mathnet.ru/vuu726}
\crossref{https://doi.org/10.35634/vm200211}
\elib{https://elibrary.ru/item.asp?id=43939877}
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    This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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    References:21
     
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