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## Archive of Issues

Russia Izhevsk
Year
2017
Volume
27
Issue
3
Pages
315-325
 Section Mathematics Title On arbitrary spectrum assignment in linear stationary systems with commensurate time delays in state variables 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 commensurate delays in state $$\dot x(t)=Ax(t)+\sum\limits_{j=1}^sA_jx(t-jh)+Bu(t),\quad y(t)=C^*x(t),\quad t>0. \qquad \qquad (1)$$ 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 UDC 517.929, 517.977 MSC 93B60, 93B55, 93B52, 93D20, 93C15, 93C05, 34H15 DOI 10.20537/vm170303 Received 20 April 2017 Language Russian Citation Zaitsev V.A., Kim I.G. On arbitrary spectrum assignment in linear stationary systems with commensurate time delays in state variables by static output feedback, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 3, pp. 315-325. References Wang Q.-G., Lee T.H., Tan K.K. Finite spectrum assignment for time-delay systems, London: Springer, 1998, 124 p. 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