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Belarus; Russia Grodno; Izhevsk
Year
2019
Volume
29
Issue
3
Pages
319-331
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Section Mathematics
Title Finite spectrum assignment problem for bilinear systems with several delays
Author(-s) Zaitsev V.A.a, Kim I.G.a, Khartovskii V.E.b
Affiliations Udmurt State Universitya, Grodno State Universityb
Abstract A bilinear control system defined by a linear stationary differential system with several non-commensurate delays in the state variable is considered. A problem of finite spectrum assignment by constant control is studied. One needs to construct constant control vectors such that the characteristic function of the closed-loop system is equal to a polynomial with arbitrary given coefficients. Conditions on coefficients of the system are obtained under which the criterion was found for solvability of the finite spectrum assignment problem. Interconnection of the criterion conditions with the property of consistency for the truncated system without delays is shown. Corollaries on stabilization of bilinear systems with delays are obtained. The similar results are obtained for discrete-time bilinear systems with several delays. An illustrative example is considered.
Keywords linear systems with delays, spectrum assignment, stabilization, bilinear system
UDC 517.929, 517.977
MSC 93B60, 93B52, 93D20, 93C15, 34H15, 93C55
DOI 10.20537/vm190303
Received 15 July 2019
Language English
Citation Zaitsev V.A., Kim I.G., Khartovskii V.E. Finite spectrum assignment problem for bilinear systems with several delays, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2019, vol. 29, issue 3, pp. 319-331.
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