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Robust Finite‐Time Stability in Stochastic Systems via Homogeneous Approximation.

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Title: Robust Finite‐Time Stability in Stochastic Systems via Homogeneous Approximation.
Authors: Braidiz, Youness1 (AUTHOR) youness.bridiz.1994@gmail.com, Kallel, Wajdi2 (AUTHOR) kallal.wajdi@gmail.com
Source: International Journal of Robust & Nonlinear Control. 5/25/2026, Vol. 36 Issue 8, p4476-4489. 14p.
Subjects: Stochastic systems, Robust stability analysis, Nonlinear dynamical systems, Approximation error, Lyapunov functions, Feedback control systems, Control theory (Engineering), Robust control
Abstract: This study extends the concept of homogeneous approximation to address homogeneous stochastic systems both at the origin and at infinity, capturing the bi‐limit behavior. We develop robust stability conditions that ensure stability for systems admitting such homogeneous approximations, even under stochastic influences. Building on this theoretical framework, we focus on the robustness of finite‐time stability in homogeneous stochastic nonlinear dynamical systems, particularly when subjected to sufficiently small affine inputs. Furthermore, we propose a robust finite‐time controller tailored for a class of affine systems, alongside a method to construct the required Lyapunov function. Specific conditions for the system's structure are provided to guarantee robust finite‐time stability. An example and simulation illustrate the effectiveness of the proposed approach, supporting its potential for advancing control strategies in complex, uncertain environments. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Robust & Nonlinear Control 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.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 192939061
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Robust Finite‐Time Stability in Stochastic Systems via Homogeneous Approximation.
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  Data: <searchLink fieldCode="AR" term="%22Braidiz%2C+Youness%22">Braidiz, Youness</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> youness.bridiz.1994@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Kallel%2C+Wajdi%22">Kallel, Wajdi</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> kallal.wajdi@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Robust+%26+Nonlinear+Control%22">International Journal of Robust & Nonlinear Control</searchLink>. 5/25/2026, Vol. 36 Issue 8, p4476-4489. 14p.
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  Data: <searchLink fieldCode="DE" term="%22Stochastic+systems%22">Stochastic systems</searchLink><br /><searchLink fieldCode="DE" term="%22Robust+stability+analysis%22">Robust stability analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+dynamical+systems%22">Nonlinear dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+error%22">Approximation error</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+functions%22">Lyapunov functions</searchLink><br /><searchLink fieldCode="DE" term="%22Feedback+control+systems%22">Feedback control systems</searchLink><br /><searchLink fieldCode="DE" term="%22Control+theory+%28Engineering%29%22">Control theory (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Robust+control%22">Robust control</searchLink>
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  Label: Abstract
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  Data: This study extends the concept of homogeneous approximation to address homogeneous stochastic systems both at the origin and at infinity, capturing the bi‐limit behavior. We develop robust stability conditions that ensure stability for systems admitting such homogeneous approximations, even under stochastic influences. Building on this theoretical framework, we focus on the robustness of finite‐time stability in homogeneous stochastic nonlinear dynamical systems, particularly when subjected to sufficiently small affine inputs. Furthermore, we propose a robust finite‐time controller tailored for a class of affine systems, alongside a method to construct the required Lyapunov function. Specific conditions for the system's structure are provided to guarantee robust finite‐time stability. An example and simulation illustrate the effectiveness of the proposed approach, supporting its potential for advancing control strategies in complex, uncertain environments. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Robust & Nonlinear Control 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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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1002/rnc.70436
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 14
        StartPage: 4476
    Subjects:
      – SubjectFull: Stochastic systems
        Type: general
      – SubjectFull: Robust stability analysis
        Type: general
      – SubjectFull: Nonlinear dynamical systems
        Type: general
      – SubjectFull: Approximation error
        Type: general
      – SubjectFull: Lyapunov functions
        Type: general
      – SubjectFull: Feedback control systems
        Type: general
      – SubjectFull: Control theory (Engineering)
        Type: general
      – SubjectFull: Robust control
        Type: general
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      – TitleFull: Robust Finite‐Time Stability in Stochastic Systems via Homogeneous Approximation.
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            NameFull: Braidiz, Youness
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            NameFull: Kallel, Wajdi
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            – D: 25
              M: 05
              Text: 5/25/2026
              Type: published
              Y: 2026
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              Value: 36
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            – TitleFull: International Journal of Robust & Nonlinear Control
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