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    This study addresses the cluster consensus problem in heterogeneous linear systems with input saturation, developing a control scheme for both leaderless and intermittently leader-pinned networks. The research provides a method to achieve guaranteed convergence rates for complex networked systems.

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    Area of Science:

    • Control Theory
    • Networked Systems
    • Systems Engineering

    Background:

    • Investigates the semiglobal cluster consensus problem for heterogeneous generic linear systems.
    • Addresses challenges posed by input saturation in control systems.
    • Considers both leaderless and intermittently leader-pinned network configurations.

    Purpose of the Study:

    • To develop a linear control scheme for achieving cluster consensus in complex systems.
    • To analyze convergence rates under specific system and network topology assumptions.
    • To extend the applicability of consensus control to systems with intermittent leader pinning.

    Main Methods:

    • Proposes a linear control scheme utilizing low-gain feedback.
    • Employs Lyapunov-based methods for convergence analysis.
    • Assumes asymptotic null controllability of individual nodes and directed spanning trees for cluster topologies.

    Main Results:

    • A control scheme is proposed for heterogeneous linear systems with input saturation.
    • Convergence analysis confirms the effectiveness of the low-gain feedback technique.
    • Explicit convergence rates are derived, dependent on control parameters and system matrices.

    Conclusions:

    • The proposed control scheme effectively solves the semiglobal cluster consensus problem.
    • The method is applicable to both leaderless and intermittently leader-pinned systems.
    • Numerical examples validate the theoretical results and the proposed control strategy.