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    Area of Science:

    • Control Systems Engineering
    • Nonlinear Systems Analysis
    • Stochastic Systems Theory

    Background:

    • Addresses the challenge of asynchronous filtering in continuous-time Takagi-Sugeno fuzzy Markov jump systems.
    • Utilizes the hidden Markov model to characterize asynchronism between filters and systems.

    Purpose of the Study:

    • To develop a robust asynchronous filter design for Takagi-Sugeno fuzzy Markov jump systems.
    • To guarantee stochastic stability and a specified dissipative performance for the filtering error system.

    Main Methods:

    • Employs a stochastic Lyapunov function to establish sufficient conditions for system stability.
    • Develops two distinct methods for the existence and design of the asynchronous filter.
    • Leverages Finsler's lemma in the second method to reduce conservatism and decision variables.

    Main Results:

    • Sufficient conditions for stochastic stability and dissipative performance are derived.
    • Two filter design approaches are presented, with the second offering reduced conservatism.
    • A numerical example validates the effectiveness and advantages of the proposed methods.

    Conclusions:

    • The proposed methods effectively address the dissipative asynchronous filtering problem for the targeted systems.
    • The Finsler's lemma-based approach provides a less conservative and more practical filter design.
    • The study contributes to the advancement of robust filtering techniques in complex dynamical systems.