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Observer Design and H∞ Performance for Discrete-Time Uncertain Fuzzy-Logic Systems.

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    This study introduces a new observer design and H∞ algorithm for discrete-time fuzzy-logic systems with uncertain parameters and unmeasurable states. The proposed piecewise fuzzy H∞ observers accurately estimate system states, improving situational awareness.

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    Area of Science:

    • Control Systems Engineering
    • Fuzzy Logic Systems
    • Advanced Mathematics

    Background:

    • Discrete-time fuzzy-logic systems often face challenges with parameter uncertainty.
    • Unmeasurable state variables hinder accurate system monitoring and control.
    • Existing observer designs may not adequately address these combined uncertainties.

    Purpose of the Study:

    • To develop an observer design and H∞ algorithm for discrete-time fuzzy-logic systems.
    • To effectively handle parameter uncertainty and unmeasurable state variables.
    • To achieve asymptotic convergence and H∞ performance for augmented systems.

    Main Methods:

    • Disintegration of the premise variable space into crisp and fuzzy regions.
    • Development of piecewise fuzzy H∞ observers based on partitioned regions.
    • Application of H∞ control algorithm for observer design.

    Main Results:

    • The proposed piecewise fuzzy H∞ observers provide accurate state estimates.
    • Improved situational awareness is achieved by addressing noncoordination and external interference.
    • The augmented systems demonstrate asymptotic convergence and H∞ performance.

    Conclusions:

    • The developed observer design and H∞ algorithm are effective for uncertain discrete-time fuzzy-logic systems.
    • Piecewise fuzzy observers enhance system understanding and performance.
    • Simulation results validate the accuracy and efficacy of the proposed approach.