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    This study develops state estimation for discrete-time memristive models using stochastic analysis. It ensures exponential mean-square stability and calculates control gain via linear matrix inequality, optimizing performance bounds.

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    Area of Science:

    • Control Systems Engineering
    • Nonlinear Dynamics
    • Materials Science

    Background:

    • Memristive devices are crucial for advanced electronics.
    • Accurate state estimation is vital for memristor-based system control.
    • Existing methods may not fully address stochastic dynamics.

    Purpose of the Study:

    • To develop a robust state estimation method for discrete-time memristive models.
    • To ensure the exponential mean-square stability of the state estimation error.
    • To derive control gain using linear matrix inequality (LMI) and optimize performance.

    Main Methods:

    • Stochastic analysis techniques applied to discrete-time memristive models.
    • Development of sufficient conditions for exponential mean-square stability.
    • Utilization of linear matrix inequality (LMI) for control gain calculation.
    • Extension to multiobjective optimization for performance bounds.

    Main Results:

    • Sufficient formulas derived for ensuring exponential mean-square stability of the error model.
    • Control gain matrix calculable via LMI.
    • Maximum bound of the active function and minimum bound of disturbance attenuation derived.
    • Simulation results validate the proposed methodology.

    Conclusions:

    • The proposed stochastic analysis provides a reliable framework for memristive model state estimation.
    • The LMI-based approach ensures system stability and allows for performance optimization.
    • This work contributes to the precise control of memristor-based systems.