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Asynchronous Dissipative Control for Fuzzy Markov Jump Systems.

Zheng-Guang Wu, Shanling Dong, Hongye Su

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    Summary
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    This study addresses asynchronous dissipative control for Takagi-Sugeno fuzzy systems with Markov jumps. A novel approach ensures stochastic stability and strict dissipativity, validated by examples.

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    Area of Science:

    • Control Theory
    • Systems Engineering
    • Fuzzy Logic Systems

    Background:

    • Investigates asynchronous dissipative control for Takagi-Sugeno fuzzy systems with Markov jump.
    • Introduces a Hidden Markov Model (HMM) to characterize controller-system nonsynchronization.

    Purpose of the Study:

    • To develop a robust asynchronous dissipative control strategy for Takagi-Sugeno fuzzy systems with Markov jump.
    • To ensure stochastic stability and strict ( , , )- -dissipative performance in the closed-loop system.

    Main Methods:

    • Employs fuzzy-basis-dependent and mode-dependent Lyapunov functions.
    • Utilizes MATLAB to solve a set of linear matrix inequalities (LMIs) for controller parameter derivation.

    Main Results:

    • Establishes a sufficient condition for stochastic stability and strict dissipativity.
    • Successfully derives controller parameters through LMI optimization.

    Conclusions:

    • The developed asynchronous dissipative control approach is valid and correct.
    • Demonstrates the effectiveness of the proposed method through two illustrative examples.