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    This study introduces a novel static output-feedback (SOF) controller design for Takagi-Sugeno fuzzy systems with constraints. The approach enhances control design flexibility and reduces conservatism for nonlinear systems.

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    Area of Science:

    • Control Systems Engineering
    • Fuzzy Logic Systems
    • Nonlinear Control Theory

    Background:

    • Takagi-Sugeno fuzzy systems are widely used for modeling nonlinear dynamics.
    • Designing static output-feedback (SOF) controllers for these systems with constraints is challenging.
    • Existing methods often lead to conservative designs.

    Purpose of the Study:

    • To propose a new SOF controller design for constrained Takagi-Sugeno fuzzy systems with nonlinear consequents.
    • To explicitly incorporate state and input constraints using set-invariance.
    • To reduce design conservatism in fuzzy SOF control.

    Main Methods:

    • Utilizing absolute stability theory and sector-bounded properties.
    • Employing set-invariance arguments for constraint handling.
    • Developing novel nonlinear SOF controllers and nonquadratic Lyapunov functions.
    • Using convexification via congruence transformations.
    • Reformulating the design as a linear matrix inequality (LMI) optimization problem.

    Main Results:

    • A generalized SOF control framework is established.
    • Nonquadratic Lyapunov functions effectively estimate potentially nonconvex domains of attraction.
    • The design is formulated as a convex optimization problem.
    • The proposed method offers greater design freedom and reduced conservatism compared to existing schemes.

    Conclusions:

    • The new approach provides a more general and less conservative method for designing SOF controllers for constrained fuzzy systems.
    • The inclusion of nonlinearities in controller and Lyapunov function design is key to improved performance.
    • The method is validated through theoretical analysis and numerical examples.