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<p>This paper’s focus is on singular infinite-dimensional systems with stochastic perturbations. Under some assumptions on the consistency of the initial condition, we discuss the existence and uniqueness of the solution. Then we determine the necessary and sufficient conditions for exponential <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^{2}\)</EquationSource> </InlineEquation>-stability. We present new findings on the robust stability of stochastically perturbed singular systems in Hilbert space. We derive new results regarding the stability radius. We obtain these via a class of operator Lyapunov equations.</p>

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New Findings Concerning the Stability Radius of Stochastic Singular Systems in Hilbert Space

  • 期刊论文

  • 发表日期：

    2026年1月2日

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  • Samah Nezzar,
  • Maissa Kada,
  • Abdelaziz Mennouni

摘要

This paper’s focus is on singular infinite-dimensional systems with stochastic perturbations. Under some assumptions on the consistency of the initial condition, we discuss the existence and uniqueness of the solution. Then we determine the necessary and sufficient conditions for exponential \(L^{2}\) -stability. We present new findings on the robust stability of stochastically perturbed singular systems in Hilbert space. We derive new results regarding the stability radius. We obtain these via a class of operator Lyapunov equations.