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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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    This study introduces novel consensus protocols for multiagent systems, achieving synchronization without requiring zero rendezvous speed. The research demonstrates effective consensus under specific connectivity conditions and gain parameters.

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    Area of Science:

    • Control Theory
    • Distributed Systems
    • Networked Systems

    Background:

    • Multiagent systems (MAS) face challenges in achieving consensus due to dynamic network topologies and communication delays.
    • Existing consensus protocols often require specific conditions like zero rendezvous speed or global information, limiting their applicability.

    Purpose of the Study:

    • To investigate the consensus problem in sampled-data second-order integrator multiagent systems.
    • To develop new consensus protocols that do not rely on absolute states and can handle switching topologies and time-varying delays.
    • To establish sufficient conditions for achieving consensus in such complex systems.

    Main Methods:

    • Design of two novel consensus protocols tailored for sampled-data systems with switching topologies and time-varying delays.
    • Analysis of system dynamics under proposed protocols to derive synchronization conditions.
    • Utilization of concepts like scrambling graph and spanning tree for analyzing network connectivity.

    Main Results:

    • The proposed protocols achieve consensus without requiring zero rendezvous speed.
    • Sufficient conditions for synchronization are derived, dependent on protocol choice and system parameters.
    • Consensus is achievable with a sufficiently small control gain and periodic joint connectivity.

    Conclusions:

    • The developed consensus protocols are effective for sampled-data second-order integrator multiagent systems with switching topology and time-varying delay.
    • The theoretical findings are validated through numerical simulations and practical examples, demonstrating the robustness of the approach.