A. V. Metel'skii, V. E. Khartovskii, O. I. Urban, “Calming the solution of systems of neutral type with many delays using feedback”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 3, 40

Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki

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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2014, Issue 3, Pages 40–51 (Mi vuu438)

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Calming the solution of systems of neutral type with many delays using feedback

A. V. Metel'skii^a, V. E. Khartovskii^b, O. I. Urban^c

^a Department of Higher Mathematics No. 1, Belarusian National Technical University, pr. Nezavisimosti, 65, Minsk, 220013, Belarus
^b Department of Logistics and Methods of Control, Yanka Kupala State University of Grodno, ul. Ozheshko, 22, Grodno, 230023, Belarus
^c Department of Mathematical Analysis and Differential Equations, Yanka Kupala State University of Grodno, ul. Ozheshko, 22, Grodno, 230023, Belarus

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Abstract: This paper examines the following problem: a linear autonomous differential-difference system of neutral type with delay in state requires ensuring its complete calming by feedback. To solve this problem linear autonomous dynamic differential-difference controller with state feedback is proposed; this controller does not exclude a closed system from the original class of linear autonomous systems of neutral type. Sufficient condition for the existence of such a controller coincides with the criterion of complete controllability. In addition, the closed system has a finite spectrum, which simplifies greatly the problem of calculating the current state during the technical implementation of the controller. The basic idea of research is to select parameters for the controller so that the closed system becomes point-degenerated in directions corresponding to phase components of the original (open) system. To do this, the original system is first converted via feedback to the single-input system of retarded type. Further, for the resulting object the dynamic controller that provides the degeneracy of the corresponding phase components is constructed.
The proposed procedure for constructing the control action is based on the algebraic properties of shift operator and does not involve calculating the roots of characteristic quasipolynomial of the original system. It can be used to provide full calming as well as exponential stability to a closed system. However, in the latter case it is necessary to use dynamic controller with state feedback of integral type.

Keywords: difference-differential system, neutral type, complete controllability, controller, feedback, point degeneration.

Received: 30.06.2014

Document Type: Article

UDC: 517.977

MSC: 93B05, 93�15

Language: Russian

Citation: A. V. Metel'skii, V. E. Khartovskii, O. I. Urban, “Calming the solution of systems of neutral type with many delays using feedback”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 3, 40–51

Citation in format AMSBIB

\Bibitem{MetKhaUrb14}

\by A.~V.~Metel'skii, V.~E.~Khartovskii, O.~I.~Urban

\paper Calming the solution of systems of neutral type with many delays using feedback

\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki

\yr 2014

\issue 3

\pages 40--51

\mathnet{http://mi.mathnet.ru/vuu438}

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This publication is cited in the following 1 articles:

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