Arbitrary finite spectrum assignment and stabilization of bilinear systems with multiple lumped and distributed delays in state
We consider a bilinear control system defined by a linear time-invariant system of differential equations with multiple lumped and distributed delays in the state variable. A problem of finite spectrum assignment is studied. One needs to construct control vectors such that the characteristic functio...
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025317 |
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| author | Vasilii Zaitsev Inna Kim |
| author_facet | Vasilii Zaitsev Inna Kim |
| author_sort | Vasilii Zaitsev |
| collection | DOAJ |
| description | We consider a bilinear control system defined by a linear time-invariant system of differential equations with multiple lumped and distributed delays in the state variable. A problem of finite spectrum assignment is studied. One needs to construct control vectors such that the characteristic function of the closed-loop system is equal to a polynomial with arbitrary given coefficients. We obtain conditions on coefficients of the system under which the criterion was found for solvability of this finite spectrum assignment problem. This criterion is expressed in terms of rank conditions for matrices of the special form. Corollaries on stabilization of a bilinear system with delays are obtained. An illustrative example is presented. |
| format | Article |
| id | doaj-art-ad74d190ee8a4127ae05be4d61e1da93 |
| institution | DOAJ |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-ad74d190ee8a4127ae05be4d61e1da932025-08-20T03:16:58ZengAIMS PressAIMS Mathematics2473-69882025-03-011036934695110.3934/math.2025317Arbitrary finite spectrum assignment and stabilization of bilinear systems with multiple lumped and distributed delays in stateVasilii Zaitsev0Inna Kim1Laboratory of Mathematical Control Theory, Udmurt State University, Izhevsk, 426034, RussiaLaboratory of Mathematical Control Theory, Udmurt State University, Izhevsk, 426034, RussiaWe consider a bilinear control system defined by a linear time-invariant system of differential equations with multiple lumped and distributed delays in the state variable. A problem of finite spectrum assignment is studied. One needs to construct control vectors such that the characteristic function of the closed-loop system is equal to a polynomial with arbitrary given coefficients. We obtain conditions on coefficients of the system under which the criterion was found for solvability of this finite spectrum assignment problem. This criterion is expressed in terms of rank conditions for matrices of the special form. Corollaries on stabilization of a bilinear system with delays are obtained. An illustrative example is presented.https://www.aimspress.com/article/doi/10.3934/math.2025317linear time-invariant differential systemtime-delay systemsspectrum assignment problemstabilizationbilinear system |
| spellingShingle | Vasilii Zaitsev Inna Kim Arbitrary finite spectrum assignment and stabilization of bilinear systems with multiple lumped and distributed delays in state AIMS Mathematics linear time-invariant differential system time-delay systems spectrum assignment problem stabilization bilinear system |
| title | Arbitrary finite spectrum assignment and stabilization of bilinear systems with multiple lumped and distributed delays in state |
| title_full | Arbitrary finite spectrum assignment and stabilization of bilinear systems with multiple lumped and distributed delays in state |
| title_fullStr | Arbitrary finite spectrum assignment and stabilization of bilinear systems with multiple lumped and distributed delays in state |
| title_full_unstemmed | Arbitrary finite spectrum assignment and stabilization of bilinear systems with multiple lumped and distributed delays in state |
| title_short | Arbitrary finite spectrum assignment and stabilization of bilinear systems with multiple lumped and distributed delays in state |
| title_sort | arbitrary finite spectrum assignment and stabilization of bilinear systems with multiple lumped and distributed delays in state |
| topic | linear time-invariant differential system time-delay systems spectrum assignment problem stabilization bilinear system |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025317 |
| work_keys_str_mv | AT vasiliizaitsev arbitraryfinitespectrumassignmentandstabilizationofbilinearsystemswithmultiplelumpedanddistributeddelaysinstate AT innakim arbitraryfinitespectrumassignmentandstabilizationofbilinearsystemswithmultiplelumpedanddistributeddelaysinstate |