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    A new fuzzy boundary sampled-data (SD) control method ensures stability for nonlinear parabolic distributed parameter systems (DPS) using Takagi-Sugeno models and linear matrix inequalities.

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    Area of Science:

    • Control Engineering
    • Applied Mathematics
    • Systems Science

    Background:

    • Nonlinear parabolic distributed parameter systems (DPS) present significant control challenges.
    • Sampled-data (SD) control is crucial for systems with discrete measurements.
    • Fuzzy logic offers a framework for handling system nonlinearities.

    Purpose of the Study:

    • To introduce a fuzzy boundary sampled-data (SD) control method for nonlinear parabolic DPS.
    • To address both distributed and boundary SD measurements.
    • To guarantee exponential stability of the controlled system.

    Main Methods:

    • Modeling the nonlinear parabolic DPS using a Takagi-Sugeno (T-S) fuzzy parabolic partial differential equation (PDE) model.
    • Designing a fuzzy boundary SD controller using linear matrix inequalities (LMIs).
    • Employing inequality techniques and a specific lemma for stability analysis.

    Main Results:

    • Development of LMI-based conditions for fuzzy boundary SD control design.
    • Demonstration of exponential stability for the closed-loop parabolic DPS.
    • Validation of the controller's effectiveness through two simulation examples.

    Conclusions:

    • The proposed fuzzy boundary SD control method effectively stabilizes nonlinear parabolic DPS.
    • The LMI-based approach provides a systematic way to design robust controllers.
    • The study contributes to the advancement of control strategies for complex distributed systems.