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    This study achieves semi-global bipartite consensus in linear multiagent systems with input saturation using low gain feedback. The method ensures convergence for homogeneous agents under specific network conditions.

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    Area of Science:

    • Control Theory
    • Systems Engineering
    • Networked Systems

    Background:

    • Bipartite consensus is crucial for coordinating multiagent systems.
    • Input saturation and directed topologies present significant control challenges.
    • Achieving consensus under these constraints requires advanced control strategies.

    Purpose of the Study:

    • To investigate the bipartite consensus problem for homogeneous linear agents with input saturation.
    • To develop a control strategy ensuring semi-global bipartite consensus.
    • To analyze the convergence properties and rate of the proposed control method.

    Main Methods:

    • Utilizing a linear feedback controller designed with low gain feedback.
    • Employing Lyapunov stability analysis for convergence verification.
    • Demonstrating theoretical findings through simulation examples.

    Main Results:

    • Semi-global bipartite consensus is achievable under structurally balanced signed digraphs with a spanning tree.
    • The proposed controller guarantees convergence for agents with asymptotic null controllability and bounded controls.
    • The Lyapunov method provides a means to determine the convergence rate.

    Conclusions:

    • The low gain feedback technique effectively addresses bipartite consensus with input saturation in linear multiagent systems.
    • The control strategy is robust under specified network and agent conditions.
    • Simulation results validate the efficacy of the theoretical framework.