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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 3, Pages 315–325 (Mi vuu591)  

MATHEMATICS

On arbitrary spectrum assignment in linear stationary systems with commensurate time delays in state variables by static output feedback

V. A. Zaitsev, I. G. Kim

Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: We consider a control system defined by a linear time-invariant system of differential equations with commensurate delays in state
\begin{equation} \dot x(t)=Ax(t)+\sum\limits_{j=1}^sA_jx(t-jh)+Bu(t),\quad y(t)=C^*x(t),\quad t>0. \tag{1} \end{equation}
We construct a controller for the system $(1)$ as linear static output feedback $u(t)=\sum\limits_{\rho =0}^{\theta}Q_\rho y(t-\rho h)$. We study an arbitrary spectrum assignment problem for the closed-loop system. One needs to define a $\theta$ and to construct gain matrices $Q_{\rho}$, $\rho=0,\ldots,\theta$, such that the characteristic function of the closed-loop system with commensurate delays becomes a quasipolynomial with arbitrary preassigned coefficients. We obtain conditions on coefficients of the system $(1)$ under which the criterion is found for solvability of the problem of arbitrary spectrum assignment. Corollaries on stabilization by linear static output feedback with commensurate delays are obtained for the system $(1)$. An illustrative example is considered.

Keywords: linear delay systems, commensurate time delays, spectrum assignment problem, stabilization, static output feedback.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00346_а
Ministry of Education and Science of the Russian Federation 1.5211.2017/8.9


DOI: https://doi.org/10.20537/vm170303

Full text: PDF file (275 kB)
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Document Type: Article
UDC: 517.929, 517.977
MSC: 93B60, 93B55, 93B52, 93D20, 93C15, 93C05, 34H15
Received: 20.04.2017

Citation: V. A. Zaitsev, I. G. Kim, “On arbitrary spectrum assignment in linear stationary systems with commensurate time delays in state variables by static output feedback”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:3 (2017), 315–325

Citation in format AMSBIB
\Bibitem{ZaiKim17}
\by V.~A.~Zaitsev, I.~G.~Kim
\paper On arbitrary spectrum assignment in linear stationary systems with commensurate time delays in state variables by static output feedback
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2017
\vol 27
\issue 3
\pages 315--325
\mathnet{http://mi.mathnet.ru/vuu591}
\crossref{https://doi.org/10.20537/vm170303}
\elib{http://elibrary.ru/item.asp?id=30267243}


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