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    Area of Science:

    • Control Theory
    • Networked Systems
    • Boolean Networks

    Background:

    • Probabilistic Boolean Control Networks (PBCNs) present complex dynamics.
    • Partial stabilization is crucial for controlling specific network behaviors.
    • Sample-data state-feedback control (SDSFC) is a practical control strategy.

    Purpose of the Study:

    • To investigate the partial stabilization problem of PBCNs under SDSFC.
    • To develop a Control Lyapunov Function (CLF) approach for PBCNs.
    • To design effective SDSFC controllers for PBCNs.

    Main Methods:

    • Representing PBCN probability structure matrix using a Boolean matrix.
    • Converting partial stabilization to global set stabilization.
    • Defining CLF and its structural matrix under SDSFC.
    • Deriving necessary and sufficient conditions for CLF existence.

    Main Results:

    • A new algebraic form for PBCNs was obtained.
    • The existence of a CLF is equivalent to the existence of an SDSFC.
    • A necessary and sufficient condition for CLF existence under SDSFC was derived.
    • Two distinct methods were presented for designing SDSFC controllers and CLF structural matrices.

    Conclusions:

    • The study provides a robust framework for partial stabilization of PBCNs using SDSFC.
    • The developed CLF approach offers a systematic way to design stabilizing controllers.
    • The findings are validated through illustrative examples, demonstrating practical applicability.