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Synchronization error estimation and controller design for delayed Lur'e systems with parameter mismatches.

Wangli He, Feng Qian, Qing-Long Han

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    This study addresses master-slave synchronization for delayed Lur

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    Area of Science:

    • Control Systems Engineering
    • Nonlinear Dynamics
    • Systems Theory

    Background:

    • Master-slave synchronization is crucial for coordinated control in complex systems.
    • Delayed Lur'e systems present unique challenges due to time delays and nonlinearities.
    • Parameter mismatches can significantly disrupt synchronization.

    Purpose of the Study:

    • To investigate master-slave synchronization of delayed Lur'e systems with parameter mismatches.
    • To establish and analyze quasi-synchronization, a synchronization with a bounded error level.
    • To design feedback controllers for achieving predetermined error levels.

    Main Methods:

    • Analysis of the synchronization error system.
    • Derivation of delay-dependent quasi-synchronization criteria.
    • Estimation of synchronization error bounds.
    • Development of feedback controllers using linear matrix inequalities (LMIs).

    Main Results:

    • Quasi-synchronization criteria were established for delayed Lur'e systems.
    • Explicit expressions for synchronization error bounds were obtained.
    • Sufficient conditions for controller existence were derived.
    • Controller gains were computed via LMIs.

    Conclusions:

    • The proposed methods effectively achieve quasi-synchronization in delayed Lur'e systems despite parameter mismatches.
    • The derived criteria and controllers offer a robust approach to synchronization problems.
    • Demonstrated effectiveness using a delayed Chua's circuit.