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    This study stabilizes uncertain stochastic Markovian jump systems (MJSs) using a novel communication protocol. The approach ensures input-to-state stability in probability (ISSiP) despite communication constraints and Rice fading.

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    Area of Science:

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

    Background:

    • Stochastic Markovian jump systems (MJSs) present challenges in stabilization due to inherent uncertainties.
    • Communication constraints, including bandwidth limitations and signal fading (Rice fading), complicate controller design for MJSs.
    • Existing methods often struggle to guarantee stability under such stringent network conditions.

    Purpose of the Study:

    • To investigate the stabilization problem of uncertain stochastic MJSs under communication constraints.
    • To develop a control strategy that accommodates limited network access and signal degradation.
    • To ensure the closed-loop system achieves input-to-state stability in probability (ISSiP).

    Main Methods:

    • A discrete-time Markovian chain is used for stochastic communication protocol (SCP) scheduling, activating one sensor node per instant.
    • A merge approach handles two Markovian chains, and a compensator provides necessary information to the controller.
    • A mode-based sliding-mode controller, combined with the compensator, is designed to achieve stability.

    Main Results:

    • The proposed control scheme ensures the closed-loop system is input-to-state stable in probability (ISSiP).
    • Quasisliding mode is attained, indicating effective system state regulation.
    • An iteration optimizing algorithm, utilizing a GA-based approach, refines the sliding gain to minimize convergence domain.

    Conclusions:

    • The developed control strategy effectively stabilizes uncertain stochastic MJSs under challenging communication constraints.
    • The integration of SCP, a compensator, and sliding-mode control offers a robust solution.
    • Simulation results validate the efficacy of the proposed GA-based sliding-mode control scheme.