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    Area of Science:

    • Control Engineering
    • Fuzzy Systems Theory
    • Nonlinear Control

    Background:

    • Takagi-Sugeno (T-S) fuzzy systems are widely used for modeling complex nonlinear systems.
    • Designing functional observer-controllers (FOC) is challenging when premise variables are unmeasurable and nonlinear.
    • Unmeasurable premise variables (UPV) introduce significant difficulties in observer and controller design.

    Purpose of the Study:

    • To develop a novel method for functional observer-controller (FOC) design in T-S fuzzy systems.
    • To address the challenge of complex, unmeasurable premise variables (UPV) with nonlinear characteristics.
    • To ensure robust stability and accurate estimation for systems with UPVs.

    Main Methods:

    • A new transformation technique is proposed to linearize the nonlinear unmeasurable premise variable (UPV).
    • The functional observer-controller (FOC) is designed to estimate the linearized premise variable.
    • Observer and controller gains are derived using convex robust and stability conditions.
    • A robust separation principle is applied to stabilize the estimation and control error system.

    Main Results:

    • The proposed transformation effectively linearizes the complex UPV.
    • The designed FOC successfully estimates the premise variable.
    • Robust stability conditions ensure the stability of the estimation and control error system.
    • Simulation examples validate the effectiveness of the developed FOC design method.

    Conclusions:

    • The presented method provides an effective solution for FOC design in T-S fuzzy systems with nonlinear UPVs.
    • The approach ensures robust stability and accurate estimation, overcoming challenges posed by unmeasurable variables.
    • This work contributes to the advancement of control strategies for complex nonlinear systems.