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Robust $ H_\infty $ resilient event-triggered control design for T-S fuzzy systems

  • * Corresponding author: Oh-Min Kwon and Rathinasamy Sakthivel

    * Corresponding author: Oh-Min Kwon and Rathinasamy Sakthivel 
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  • This paper investigates the resilient $ H_\infty $ event-triggered control problem for Takagi-Sugeno fuzzy system with time-varying delay and external disturbance. Contrary to some existing results, the considered event-triggered conditions are verified only at each sampling instant because it is difficult to prove Zeno-freeness for a continuous event-triggered mechanism in the presence of external disturbance. Furthermore, by constructing an appropriate Lyapunov-Krasovskii functional, sufficient conditions are derived in the form of linear matrix inequalities to ensure the asymptotic stability and the $ H_\infty $ performances of closed-loop systems. More precisely, the proposed control design not only improve robust performance but also save the communication resources. Finally, the obtained theoretical results are verified through numerical simulation, which demonstrate the efficiency and advantages of the proposed method.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

    Citation:

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  • Figure 1.  State responses curve of T-S fuzzy system (1) with control

    Figure 2.  State responses curve of T-S fuzzy system (1) without control

    Figure 3.  Control Curve

    Figure 4.  The event-triggered instants and intervals

    Figure 5.  State responses curve of T-S fuzzy system (1) with control

    Figure 6.  State responses curve of T-S fuzzy system (1) without control

    Figure 7.  Control responses

    Figure 8.  The event-triggered instants and intervals

    Table 1.  Calculated upper bound of $ \bar{k} $ for different values of $ \delta $

    $ \delta $ 0.05 0.08 0.10 0.15 0.18
    $ \bar{k} $ 0.3410 0.3312 0.3201 0.3050 0.3016
     | Show Table
    DownLoad: CSV

    Table 2.  Calculated minimum value of $ \gamma $ for various values of $ \bar{k} $

    $ \bar{k} $ 0.1 0.13 0.15 0.25 0.30
    $ \gamma $ 0.2236 0.2491 0.2743 0.6646 1.6538
     | Show Table
    DownLoad: CSV
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