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<p>This paper investigates the admissibility and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(H_\infty\)</EquationSource> </InlineEquation> control of two-dimensional (2D) continuous singular systems described by Singular Roesser Models (SRMs). Our novel approach transforms any 2D SRM system into an equivalent, easier-to-analyze form while preserving its properties. We reformulate the control input to enable independent control of each dynamic, offering extensive control possibilities. The admissibility of the open-loop system, including acceptability, non-impulsiveness, and stability, is investigated. An <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(H_\infty\)</EquationSource> </InlineEquation> static state-feedback (SSF) controller is designed using Linear Matrix Inequalities (LMIs), solving a strict LMI condition to ensure closed-loop admissibility and specified performance. The effectiveness of the proposed method is demonstrated through two numerical examples, which highlight significant improvements over existing approaches. The results confirm both the robustness and practical feasibility of the method across a wide range of parameters, underscoring its broader applicability.</p>

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Two-Dimensional Singular Continuous Systems, Admissibility Analysis and \(H_\infty\) Control

  • 期刊论文

  • 发表日期：

    2025年12月4日

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  • Abderrahim El Asraoui,
  • Abdelaziz Hmamed,
  • Bensalem Boukili,
  • Noreddine Chaibi

摘要

This paper investigates the admissibility and \(H_\infty\) control of two-dimensional (2D) continuous singular systems described by Singular Roesser Models (SRMs). Our novel approach transforms any 2D SRM system into an equivalent, easier-to-analyze form while preserving its properties. We reformulate the control input to enable independent control of each dynamic, offering extensive control possibilities. The admissibility of the open-loop system, including acceptability, non-impulsiveness, and stability, is investigated. An \(H_\infty\) static state-feedback (SSF) controller is designed using Linear Matrix Inequalities (LMIs), solving a strict LMI condition to ensure closed-loop admissibility and specified performance. The effectiveness of the proposed method is demonstrated through two numerical examples, which highlight significant improvements over existing approaches. The results confirm both the robustness and practical feasibility of the method across a wide range of parameters, underscoring its broader applicability.