Abstract
For a spectrally controlled linear time-invariant delay system with commensurable delays, we construct a static state feedback ensuring an arbitrary finite spectrum of the closedloop system. By an appropriate choice of the spectrum, one can make the closed-loop system asymptotically stable. The results are illustrated by examples.
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Manitius, A.Z. and Olbrot, A.W., Finite Spectrum Assignment Problem for Systems with Delays, IEEE Trans. Automat. Control, 1979. AC-24, no. 4, pp. 541–553.
Krasovskii, N.N. and Osipov, Yu.S., On Stabilization of the Motion of a Plant with Delay in the Control System, Izv. Akad. Nauk SSSR Tekhn. Kibern., 1963, no. 6, pp. 3–15.
Osipov, Yu.S., On Stabilization of Control Systems with Delay, Differ. Uravn., 1965, vol. 1, no. 5, pp. 605–618.
Bulatov, V.I., Spectral Reducibility of Systems with Lag, Vestn. Belarus. Univ. Ser. 1, 1979, no. 3, pp. 78–80.
Karpuk, V.V. and Metel’skii, A.V., Complete Damping and Stabilization of Linear Autonomous Systems with Delay, Izv. Ross. Akad. Nauk Teor. Sist. Upravl., 2009, no. 6, pp. 19–28.
Bhat, K.P. and Koivo, H.N., Model Characterization of Controllability and Observability of Time-Delay Systems, IEEE Trans. Automat. Control, 1976. AC-21, no. 2, pp. 292–293.
Marchenko, V.M., On the Controllability of Linear Systems with Delay, Dokl. Akad. Nauk SSSR, 1977, vol. 236, no. 5, pp. 1083–1086.
Watanabe, K., Ito, M., and Kaneko, M., Finite Spectrum Assignment Problem for Systems with Multiple Commensurate Delays in State Variables, Internat. J. Control, 1983, vol. 38, no. 5, pp. 913–926.
Bulatov, V.I., Spectral Controllability of Systems with Lag, Differ. Uravn., 1977, vol. 13, no. 10, pp. 1876–1888.
Metel’skii, A.V., Spectral Reducibility of Differential Systems with Delay Using a Dynamic Controller, Differ. Uravn., 2011, vol. 47, no. 11, pp. 1621–1637.
Manitius, A. and Triggiani, R., Function Space Controllability of Linear Retarded Systems: a Derivation from Abstract Operator Conditions, SIAM J. Control Optim., 1978, vol. 16, no. 4, pp. 599–643.
Metel’skii, A.V., Spectral Reduction, Complete Damping, and Stabilization of a Delay System by a Single Controller, Differ. Uravn., 2013, vol. 49, no. 11, pp. 1436–1452.
Gantmakher, F.R., Teoriya matrits (Theory of Matrices), Moscow: Nauka, 1988.
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Original Russian Text © A.V. Metel’skii, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 5, pp. 692–701.
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Metel’skii, A.V. Finite spectrum assignment problem for a delay type system. Diff Equat 50, 689–699 (2014). https://doi.org/10.1134/S0012266114050115
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DOI: https://doi.org/10.1134/S0012266114050115