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<p>Focusing on linear multiple-input-multiple-output (MIMO) stochastic parabolic partial difference systems with time delay, this paper investigates their mean-square exponential stability conditions and develops stabilization via both state feedback and reduced-order dynamic output feedback controllers. A definition of mean-square exponential stability is established as the foundation for the subsequent analysis. To address the challenges posed by time delay terms in the stability proof, an auxiliary function is constructed that produces an inequality connecting the mean-square expectation in the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {L}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">L</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-norm with exponential decay rates and the supremum of the initial state. Sufficient conditions for mean-square exponential stability and stabilization are proposed based on the system matrices. Finally, the theoretical results are validated by numerical simulations.</p>

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Mean-square exponential stability and stabilization for linear MIMO stochastic parabolic partial difference systems with time delay

  • 期刊论文

  • 发表日期：

    2026年3月27日

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  • Xisheng Dai,
  • Shangyu Yong,
  • Jinhua Huang

摘要

Focusing on linear multiple-input-multiple-output (MIMO) stochastic parabolic partial difference systems with time delay, this paper investigates their mean-square exponential stability conditions and develops stabilization via both state feedback and reduced-order dynamic output feedback controllers. A definition of mean-square exponential stability is established as the foundation for the subsequent analysis. To address the challenges posed by time delay terms in the stability proof, an auxiliary function is constructed that produces an inequality connecting the mean-square expectation in the \(\mathbb {L}^2\) L 2 -norm with exponential decay rates and the supremum of the initial state. Sufficient conditions for mean-square exponential stability and stabilization are proposed based on the system matrices. Finally, the theoretical results are validated by numerical simulations.