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<p>The primary objective of this article is to investigate the consensus problem of nonlinear stochastic delay multi-agent systems driven by Lévy processes under an event-triggered communication mechanism over directed graphs. The study particularly emphasizes addressing the dual challenges of ensuring system stability in the stochastic setting and improving communication efficiency. To this end, a novel adaptive event-triggered strategy based on neighboring information is developed, which significantly reduces communication frequency while guaranteeing a strictly positive lower bound between successive triggering instants, thereby excluding Zeno behavior. To facilitate the analysis, a coordinate transformation is introduced, transforming the original delayed system into an equivalent form with tractable eigenvalue properties. Furthermore, by employing It<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\hat{\textrm{o}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mtext>o</mtext> <mo stretchy="false">^</mo> </mover> </math></EquationSource> </InlineEquation> stochastic differential theory, rigorous stability conditions for the closed-loop system are established under mild assumptions. Leveraging the It<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\hat{\textrm{o}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mtext>o</mtext> <mo stretchy="false">^</mo> </mover> </math></EquationSource> </InlineEquation> isometry and nonnegative matrix theory, it is further shown that the sampling errors decay exponentially to zero, leading to mean-square consensus. Unlike most existing studies that rely only on Brownian-motion-driven systems, the present work investigates event-triggered consensus in the presence of Lévy processes while also accounting for communication delays. Finally, a numerical simulation is conducted to validate the effectiveness of the proposed theoretical results.</p>

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Exponential consensus of stochastic delayed multi-agent systems with Lévy noise under event-triggered control

  • 期刊论文

  • 发表日期：

    2026年4月20日

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  • Haokun Hu,
  • Quanxin Zhu

摘要

The primary objective of this article is to investigate the consensus problem of nonlinear stochastic delay multi-agent systems driven by Lévy processes under an event-triggered communication mechanism over directed graphs. The study particularly emphasizes addressing the dual challenges of ensuring system stability in the stochastic setting and improving communication efficiency. To this end, a novel adaptive event-triggered strategy based on neighboring information is developed, which significantly reduces communication frequency while guaranteeing a strictly positive lower bound between successive triggering instants, thereby excluding Zeno behavior. To facilitate the analysis, a coordinate transformation is introduced, transforming the original delayed system into an equivalent form with tractable eigenvalue properties. Furthermore, by employing It \(\hat{\textrm{o}}\) o ^ stochastic differential theory, rigorous stability conditions for the closed-loop system are established under mild assumptions. Leveraging the It \(\hat{\textrm{o}}\) o ^ isometry and nonnegative matrix theory, it is further shown that the sampling errors decay exponentially to zero, leading to mean-square consensus. Unlike most existing studies that rely only on Brownian-motion-driven systems, the present work investigates event-triggered consensus in the presence of Lévy processes while also accounting for communication delays. Finally, a numerical simulation is conducted to validate the effectiveness of the proposed theoretical results.