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    This study introduces a new method for state estimation in 2-D Markov jumping systems facing false data injection attacks. The approach enhances system robustness and adaptability for reliable performance.

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    Area of Science:

    • Control Systems Engineering
    • Signal Processing
    • Cybersecurity in Systems

    Background:

    • State estimation is crucial for 2-D Markov jumping systems.
    • Randomly occurring False Data Injection Attacks (FDIA) pose significant threats to system integrity and performance.
    • Existing methods may lack robustness against dynamic network conditions and sophisticated attacks.

    Purpose of the Study:

    • To develop a robust state estimation method for 2-D Markov jumping systems under FDIA.
    • To enhance system adaptability and performance in uncertain network environments.
    • To guarantee stability and noise attenuation despite malicious data injection.

    Main Methods:

    • Proposed a novel probabilistic multi-interval event-triggering mechanism (PMIETP) combining subinterval thresholds and probability models.
    • Developed a time-varying saturation mechanism (TVSM)-based estimator with an adaptive threshold to handle abnormal data.
    • Utilized Particle Swarm Optimization (PSO) to optimize design parameters and reduce conservativeness in linear matrix inequality (LMI) conditions.
    • Derived sufficient criteria based on Lyapunov stability theory for mean-square asymptotic stability and noise attenuation.

    Main Results:

    • The proposed PMIETP integrated with TVSM effectively mitigates the impact of FDIA.
    • The approach demonstrates enhanced adaptability to varying network conditions and improved estimation robustness.
    • Numerical simulations confirm the effectiveness and superiority of the proposed method over existing techniques.

    Conclusions:

    • The novel PMIETP and TVSM-based state estimation approach provides a robust solution for 2-D Markov jumping systems under FDIA.
    • The method ensures system stability and performance guarantees, offering significant advantages in practical applications.
    • The study highlights the potential of adaptive mechanisms and optimization algorithms in enhancing the security of control systems.