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    Area of Science:

    • Control Systems Engineering
    • Stochastic Systems Analysis
    • Networked Control Systems

    Background:

    • Networked Control Systems (NCSs) face challenges from network-induced constraints like quantization and stochastic protocols.
    • Discrete-time nonlinear stochastic systems with exogenous disturbances require robust stabilization methods.
    • Observer-based control is crucial for systems where states are not directly measurable.

    Purpose of the Study:

    • To investigate the observer-based stabilization problem for discrete-time nonlinear stochastic NCSs.
    • To account for uniform quantization and stochastic communication protocols (SCP) in signal transmission.
    • To introduce and analyze input-to-state stability in probability for the closed-loop system.

    Main Methods:

    • Development of a theoretical framework using switched Lyapunov function method and stochastic analysis techniques.
    • Characterization of system dynamics via nonlinear stochastic difference equations with Markovian jumping parameters.
    • Derivation of observer-based controller existence conditions and explicit gain matrix expressions.

    Main Results:

    • Established conditions for observer-based controller existence ensuring input-to-state stability in probability.
    • Provided explicit expressions for the gain matrices of the designed controller.
    • Demonstrated the effectiveness of the proposed theoretical results through a numerical simulation example.

    Conclusions:

    • The proposed observer-based control strategy effectively stabilizes discrete-time nonlinear stochastic NCSs under network constraints.
    • Input-to-state stability in probability is achieved by utilizing quantized measurements and SCP scheduling.
    • The methodology provides a robust framework for designing controllers for complex networked systems.