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A New Approach to Modeling and Stabilizing 2-D Markovian FMII Systems.

Xinyu Lv, Yugang Niu, James Lam

    IEEE Transactions on Cybernetics
    |May 15, 2026
    PubMed
    Summary
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    This study introduces novel 2-D Markovian Fornasini-Marchesini (FMII) system models for improved stability analysis. The new approach enhances modeling by considering mode relationships and directional influences for better dynamic behavior prediction.

    Area of Science:

    • Control Theory
    • Stochastic Systems
    • Systems Engineering

    Background:

    • Existing 2-D Markovian systems lack comprehensive modeling of mode relationships.
    • Fornasini-Marchesini (FMII) systems require advanced methods for stability analysis.
    • Directional influences and mode dependencies are crucial for accurate system dynamics.

    Purpose of the Study:

    • To propose a novel approach for modeling and stabilizing 2-D Markovian Fornasini-Marchesini (FMII) systems.
    • To develop new 2-D Markov chains that capture joint mode determination from preceding states.
    • To provide stability conditions and stabilization methods for both autonomous and controlled FMII systems.

    Main Methods:

    • Development of two new 2-D Markov chains with distinct classification criteria for mode relationships.

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  • Reclassification of mode combinations to ensure joint determination of the current mode by two preceding modes.
  • Design of transition probabilities for asymptotic stability in the mean square and asynchronous controllers for stabilization.

    • Main Results:

    • Established new 2-D Markovian FMII system models that effectively capture dynamic behavior.
    • Provided sufficient conditions for asymptotic stability in the mean square for autonomous systems.
    • Addressed the stabilization of controlled systems by designing transition probabilities and asynchronous controllers simultaneously.

    Conclusions:

    • The proposed modeling approach accurately reflects the dynamic behavior of 2-D FMII systems.
    • The developed conditions ensure asymptotic stability in the mean square for autonomous systems.
    • Simultaneous design of transition probabilities and controllers enables effective stabilization of controlled 2-D Markovian FMII systems.