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Sufficient and necessary conditions for exponential stabilisation of distributed second-order bilinear systems with time-varying delay.

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Title: Sufficient and necessary conditions for exponential stabilisation of distributed second-order bilinear systems with time-varying delay.
Authors: Tsouli, A.1 (AUTHOR), Ghilli, O.1 (AUTHOR), Ouarit, M.2 (AUTHOR) ghilli.otmane1993@gmail.com
Source: Journal of Control & Decision. Jul2026, Vol. 13 Issue 4, p1196-1208. 13p.
Subjects: Exponential stability, Distributed parameter systems, Time delay systems, Feedback control systems, Hilbert space, Controllability in systems engineering
Abstract: In this paper, we deal with the problem of exponential stabilisation for a class of distributed second-order bilinear systems. The systems under consideration come with a time-varying delay and are evolving in a Hilbert space. A new stabilising feedback law is proposed. Existence and uniqueness of the mild solution for the controlled system are proved. Moreover, under a new controllability condition which is both sufficient and necessary, we establish exponential stabilisation results and provide an explicit decay rate estimate. Some illustrating applications are displayed. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Control & Decision is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Sufficient and necessary conditions for exponential stabilisation of distributed second-order bilinear systems with time-varying delay.
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  Data: <searchLink fieldCode="AR" term="%22Tsouli%2C+A%2E%22">Tsouli, A.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ghilli%2C+O%2E%22">Ghilli, O.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ouarit%2C+M%2E%22">Ouarit, M.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> ghilli.otmane1993@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Control+%26+Decision%22">Journal of Control & Decision</searchLink>. Jul2026, Vol. 13 Issue 4, p1196-1208. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Exponential+stability%22">Exponential stability</searchLink><br /><searchLink fieldCode="DE" term="%22Distributed+parameter+systems%22">Distributed parameter systems</searchLink><br /><searchLink fieldCode="DE" term="%22Time+delay+systems%22">Time delay systems</searchLink><br /><searchLink fieldCode="DE" term="%22Feedback+control+systems%22">Feedback control systems</searchLink><br /><searchLink fieldCode="DE" term="%22Hilbert+space%22">Hilbert space</searchLink><br /><searchLink fieldCode="DE" term="%22Controllability+in+systems+engineering%22">Controllability in systems engineering</searchLink>
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  Label: Abstract
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  Data: In this paper, we deal with the problem of exponential stabilisation for a class of distributed second-order bilinear systems. The systems under consideration come with a time-varying delay and are evolving in a Hilbert space. A new stabilising feedback law is proposed. Existence and uniqueness of the mild solution for the controlled system are proved. Moreover, under a new controllability condition which is both sufficient and necessary, we establish exponential stabilisation results and provide an explicit decay rate estimate. Some illustrating applications are displayed. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Control & Decision is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1080/23307706.2025.2511685
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      – Code: eng
        Text: English
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        PageCount: 13
        StartPage: 1196
    Subjects:
      – SubjectFull: Exponential stability
        Type: general
      – SubjectFull: Distributed parameter systems
        Type: general
      – SubjectFull: Time delay systems
        Type: general
      – SubjectFull: Feedback control systems
        Type: general
      – SubjectFull: Hilbert space
        Type: general
      – SubjectFull: Controllability in systems engineering
        Type: general
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      – TitleFull: Sufficient and necessary conditions for exponential stabilisation of distributed second-order bilinear systems with time-varying delay.
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              M: 07
              Text: Jul2026
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              Y: 2026
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