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    This study introduces a new method for containment control in multiagent systems, ensuring follower agents coordinate with leaders despite disturbances. A novel observer and control protocol achieve reliable containment coordination.

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    Area of Science:

    • Control Systems Engineering
    • Robotics
    • Networked Systems

    Background:

    • Multiagent systems require coordinated behavior for tasks.
    • Containment control ensures follower agents remain within a region defined by leaders.
    • External disturbances can disrupt coordination in real-world applications.

    Purpose of the Study:

    • To develop a robust containment control strategy for continuous-time multiagent systems.
    • To design an observer capable of estimating system states under disturbances.
    • To ensure reliable containment coordination between leader and follower agents.

    Main Methods:

    • A containment error metric was defined to quantify coordination.
    • A reduced-order observer was designed using neighbor observable convex hull states.
    • A reduced-order control protocol was developed to address external disturbances.
    • A novel approach to solving a Sylvester equation was used to validate the control protocol.

    Main Results:

    • The designed observer and control protocol effectively achieve containment coordination.
    • The study proves the solvability of the associated Sylvester equation.
    • A numerical example validated the theoretical results.

    Conclusions:

    • The proposed method offers a robust solution for containment control in disturbed multiagent systems.
    • The novel approach to Sylvester equations contributes to control theory.
    • The findings are applicable to various multiagent coordination tasks.