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Home » Issues » Archive of Issues » 2016 - 4 issue » pp. 463-473

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Russia Izhevsk
Year
2016
Volume
26
Issue
4
Pages
463-473
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Section Mathematics
Title Finite spectrum assignment problem in linear systems with state delay by static output feedback
Author(-s) Zaitsev V.A.a, Kim I.G.a
Affiliations Udmurt State Universitya
Abstract We consider a control system defined by a linear time-invariant system of differential equations with delay $$ \dot x(t)=Ax(t)+A_1x(t-h)+Bu(t),\quad y(t)=C^*x(t),\quad t>0. \qquad\qquad (1) $$ We construct the controller for the system $(1)$ as linear output feedback $u(t)=Q_0 y(t)+Q_1 y(t-h)$. We study a finite spectrum assignment problem for the closed-loop system. One needs to construct gain matrices $Q_0$, $Q_1$ such that the characteristic quasipolynomial of the closed-loop system becomes a polynomial with arbitrary preassigned coefficients. We obtain conditions on coefficients of the system $(1)$ under which the criterion was found for solvability of the finite spectrum assignment problem. The obtained result extends to systems with several delays. Corollaries on stabilization by linear static output feedback with delay are obtained for system $(1)$ as well as for systems of type $(1)$ with several delays.
Keywords linear delay systems, spectrum assignment, stabilization, output feedback
UDC 517.929, 517.977
MSC 93B60, 93B55, 93B52, 93D20, 93C15, 93C05, 34H15
DOI 10.20537/vm160402
Received 1 October 2016
Language Russian
Citation Zaitsev V.A., Kim I.G. Finite spectrum assignment problem in linear systems with state delay by static output feedback, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 4, pp. 463-473.
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