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Linear Programming Approach to Constrained Stabilization of Positive Differential‐Difference Equations With Unbounded Delay.

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Title: Linear Programming Approach to Constrained Stabilization of Positive Differential‐Difference Equations With Unbounded Delay.
Authors: Sau, N. H.1 (AUTHOR), Niamsup, P.2 (AUTHOR), Phat, V. N.3 (AUTHOR) vnphat@math.ac.vn
Source: Optimal Control - Applications & Methods. Nov2025, Vol. 46 Issue 6, p2581-2594. 14p.
Subjects: Linear programming, Differential-difference equations, Robust control, Feedback control systems, Global asymptotic stability, Control theory (Engineering), State feedback (Feedback control systems)
Abstract: This article addresses the constrained stabilization problem for a class of linear positive differential‐difference equations (DDEs) characterized by unbounded time‐varying delays and subject to bounded control constraints. We propose an efficient methodology rooted in linear programming (LP) to design stabilizing state feedback controllers. The core contributions include the development of novel characterizations for system positivity and the comparison principle tailored to this specific class of DDEs. Based on these characterizations, we establish sufficient conditions for the existence of admissible state feedback controllers that guarantee both positivity and asymptotic stability of the closed‐loop system while respecting the control input constraints. Crucially, these conditions are formulated as a set of linear inequalities, rendering the controller design problem solvable via standard LP techniques. The effectiveness and practical applicability of the theoretical results are demonstrated through comprehensive numerical examples. [ABSTRACT FROM AUTHOR]
Copyright of Optimal Control - Applications & Methods is the property of Wiley-Blackwell 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: Linear Programming Approach to Constrained Stabilization of Positive Differential‐Difference Equations With Unbounded Delay.
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  Data: <searchLink fieldCode="JN" term="%22Optimal+Control+-+Applications+%26+Methods%22">Optimal Control - Applications & Methods</searchLink>. Nov2025, Vol. 46 Issue 6, p2581-2594. 14p.
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  Data: <searchLink fieldCode="DE" term="%22Linear+programming%22">Linear programming</searchLink><br /><searchLink fieldCode="DE" term="%22Differential-difference+equations%22">Differential-difference equations</searchLink><br /><searchLink fieldCode="DE" term="%22Robust+control%22">Robust control</searchLink><br /><searchLink fieldCode="DE" term="%22Feedback+control+systems%22">Feedback control systems</searchLink><br /><searchLink fieldCode="DE" term="%22Global+asymptotic+stability%22">Global asymptotic stability</searchLink><br /><searchLink fieldCode="DE" term="%22Control+theory+%28Engineering%29%22">Control theory (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22State+feedback+%28Feedback+control+systems%29%22">State feedback (Feedback control systems)</searchLink>
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  Data: This article addresses the constrained stabilization problem for a class of linear positive differential‐difference equations (DDEs) characterized by unbounded time‐varying delays and subject to bounded control constraints. We propose an efficient methodology rooted in linear programming (LP) to design stabilizing state feedback controllers. The core contributions include the development of novel characterizations for system positivity and the comparison principle tailored to this specific class of DDEs. Based on these characterizations, we establish sufficient conditions for the existence of admissible state feedback controllers that guarantee both positivity and asymptotic stability of the closed‐loop system while respecting the control input constraints. Crucially, these conditions are formulated as a set of linear inequalities, rendering the controller design problem solvable via standard LP techniques. The effectiveness and practical applicability of the theoretical results are demonstrated through comprehensive numerical examples. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Optimal Control - Applications & Methods is the property of Wiley-Blackwell 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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        Value: 10.1002/oca.70015
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      – Code: eng
        Text: English
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        PageCount: 14
        StartPage: 2581
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      – SubjectFull: Linear programming
        Type: general
      – SubjectFull: Differential-difference equations
        Type: general
      – SubjectFull: Robust control
        Type: general
      – SubjectFull: Feedback control systems
        Type: general
      – SubjectFull: Global asymptotic stability
        Type: general
      – SubjectFull: Control theory (Engineering)
        Type: general
      – SubjectFull: State feedback (Feedback control systems)
        Type: general
    Titles:
      – TitleFull: Linear Programming Approach to Constrained Stabilization of Positive Differential‐Difference Equations With Unbounded Delay.
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            NameFull: Sau, N. H.
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            NameFull: Niamsup, P.
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            NameFull: Phat, V. N.
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            – D: 01
              M: 11
              Text: Nov2025
              Type: published
              Y: 2025
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