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<p>This paper investigates the leader-following consensus (L-FC) of multi-agent systems with nonlinear dynamics and semi-Markov jump process via sampled-data control. First, by introducing several scalar parameters, an improved reciprocally convex inequality (RCI) is established, which provides a tight bound for reciprocally convex combinations. This inequality includes&#xa0;some known ones as its special cases. Second, considering randomly occurring controller gain fluctuations, more applicable nonfragile memory sampled-data controllers are designed with the signal transmission delay. Then, instead of the general quadratic type of the Lyapunov–Krasovskii functional, a new two-sided looped functional is constructed by applying the sampling- instant-to-present-time fragment approach, which utilizes more information of inner sampling behavior and weakens the positive definite constraint in the entire time domain to the sampled instants. Next, a few sufficient conditions are derived to achieve the L-FC based on the presented improved RCI. Finally, a numerical example illustrates the effectiveness and advantages of the obtained method.</p>

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Sampled-data consensus tracking of nonlinear semi-Markovian multi-agent systems via improved reciprocally convex inequality

  • 期刊论文

  • 发表日期：

    2025年5月12日

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  • Yan Zhao,
  • Cheng-De Zheng

摘要

This paper investigates the leader-following consensus (L-FC) of multi-agent systems with nonlinear dynamics and semi-Markov jump process via sampled-data control. First, by introducing several scalar parameters, an improved reciprocally convex inequality (RCI) is established, which provides a tight bound for reciprocally convex combinations. This inequality includes some known ones as its special cases. Second, considering randomly occurring controller gain fluctuations, more applicable nonfragile memory sampled-data controllers are designed with the signal transmission delay. Then, instead of the general quadratic type of the Lyapunov–Krasovskii functional, a new two-sided looped functional is constructed by applying the sampling- instant-to-present-time fragment approach, which utilizes more information of inner sampling behavior and weakens the positive definite constraint in the entire time domain to the sampled instants. Next, a few sufficient conditions are derived to achieve the L-FC based on the presented improved RCI. Finally, a numerical example illustrates the effectiveness and advantages of the obtained method.