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    Area of Science:

    • Control Systems Engineering
    • Networked Systems
    • Robotics

    Background:

    • Position-based control protocols typically fail to achieve synchronization in networked harmonic oscillators.
    • Network-induced delays are often considered detrimental to system synchronization.

    Purpose of the Study:

    • To investigate the potential positive impact of network-induced delays on the synchronization of networked harmonic oscillators.
    • To develop a position-based control protocol that leverages delays for synchronization.

    Main Methods:

    • Harmonic oscillators connected via a digital communication network with asynchronous sampling.
    • Time-varying, bounded, and unsynchronized network-induced delays are considered.
    • A buffer is embedded in each controller to manage sampled data.
    • The synchronization error system is modeled as a linear system with multiple interval time-varying delays.
    • Discretized Lyapunov-Krasovskii functional method is employed to derive stability conditions.

    Main Results:

    • A sufficient condition for the asymptotic stability of the synchronization error system is derived.
    • This condition ensures synchronization for network-induced delays within a specific positive interval.
    • Control protocols are designed using linear matrix inequalities (LMIs) with tunable parameters.

    Conclusions:

    • Network-induced delays can be effectively utilized to achieve synchronization in networked harmonic oscillators.
    • The proposed position-based control strategy, accounting for delays and asynchronous sampling, is validated.
    • The method's effectiveness is demonstrated on a multi-robot platform.