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    Area of Science:

    • Control Systems Engineering
    • Stochastic Systems Analysis
    • Advanced Mathematics

    Background:

    • Addresses the challenge of asynchronous control in 2-D Markov jump systems (MJSs).
    • Considers practical limitations such as unobservable system modes and uncertain transition probabilities (TPs).

    Purpose of the Study:

    • To develop novel control strategies for 2-D MJSs with nonideal TPs and hidden modes.
    • To ensure asymptotic mean square stability with guaranteed H∞ performance.

    Main Methods:

    • Employs a hidden Markov model (HMM) to handle mismatched modes between the system and its observation.
    • Utilizes a nonconservative separation strategy to decouple system and observation TPs.
    • Develops a unified Linear Matrix Inequality (LMI) based condition for analysis.

    Main Results:

    • Presents new sufficient conditions for asymptotic mean square stability and H∞ performance.
    • Demonstrates reduced conservatism compared to existing methods in the literature.
    • Validates the proposed approach through two illustrative examples.

    Conclusions:

    • The developed method effectively handles asynchronous control for 2-D MJSs with nonideal TPs and hidden modes.
    • The unified LMI-based condition offers a more conservative and practical solution.
    • The findings advance the stability analysis and control design for complex stochastic systems.