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<p>This paper investigates the problem of matrix-scaled consensus in multi-agent systems with time-varying delays. In contrast to conventional consensus problems where agents converge to a constant value, we consider a more general scenario in which the consensus value follows an arbitrary time-varying reference function. Both uniform and slowly time-varying delay cases are analyzed within the matrix-scaled consensus tracking (MSCT) framework. The proposed approach is developed using the Lyapunov–Krasovskii theorem in conjunction with extended Jensen and Wirtinger inequalities, leading to the derivation of delay-dependent stability conditions formulated as linear matrix inequalities (LMIs). The admissible time-delay bounds and the allowable rate of delay variation are explicitly determined. Numerical simulation examples are provided to validate the effectiveness and reduced conservatism of the proposed method.</p>

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Matrix-Scaled Consensus of Multi-agent Systems with Time-Varying Delay

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Hoang Huy Vu,
  • Dung Dinh Le,
  • Van Nam Giap,
  • Nam Hoai Nguyen,
  • Tuynh Van Pham

摘要

This paper investigates the problem of matrix-scaled consensus in multi-agent systems with time-varying delays. In contrast to conventional consensus problems where agents converge to a constant value, we consider a more general scenario in which the consensus value follows an arbitrary time-varying reference function. Both uniform and slowly time-varying delay cases are analyzed within the matrix-scaled consensus tracking (MSCT) framework. The proposed approach is developed using the Lyapunov–Krasovskii theorem in conjunction with extended Jensen and Wirtinger inequalities, leading to the derivation of delay-dependent stability conditions formulated as linear matrix inequalities (LMIs). The admissible time-delay bounds and the allowable rate of delay variation are explicitly determined. Numerical simulation examples are provided to validate the effectiveness and reduced conservatism of the proposed method.