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    This study analyzes lag consensus in multiagent systems using Lyapunov functional and matrix theory. It identifies optimal pinning strategies and coupling strengths for achieving consensus, even in noisy conditions.

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    Area of Science:

    • Control Theory
    • Systems Engineering
    • Nonlinear Dynamics

    Background:

    • Multiagent systems (MAS) are crucial for distributed tasks.
    • Lag consensus involves followers synchronizing with a time delay.
    • Controlling MAS for consensus is an active research area.

    Purpose of the Study:

    • To investigate pinning-controlled lag consensus in second-order nonlinear MAS.
    • To determine optimal agent pinning and coupling strengths for achieving lag consensus.
    • To address the challenges of lag consensus in noisy environments.

    Main Methods:

    • Application of Lyapunov functional for stability analysis.
    • Utilization of matrix theory to analyze system dynamics.
    • Development of a pinning control protocol.

    Main Results:

    • Identification of key agents for pinning to achieve lag consensus.
    • Determination of appropriate coupling strengths for system synchronization.
    • Demonstration of control protocol effectiveness in simulations, including noisy scenarios.

    Conclusions:

    • The proposed pinning control strategy effectively achieves lag consensus in second-order nonlinear MAS.
    • The study provides a framework for selecting pinning agents and coupling strengths.
    • The findings are robust and applicable to practical systems with environmental noise.