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Sliding mode control for uncertain T-S fuzzy systems with input and state delays

  • * Corresponding author: Ruxia Zhang

    * Corresponding author: Ruxia Zhang 
The first author is supported by is supported by National Nature Science Foundation under grant NO.61673099 and Provincial Education Department Key Project (LZGD2017039)
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  • In this paper, the problem of sliding mode control (SMC) for uncertain T-S (Tagaki-Sugeno) fuzzy systems with input and state delays is investigated, in which the nonlinear uncertain terms are unknown, and also unmatched. For the T-S fuzzy model of the controlled object, a method based on sliding mode compensator is designed, and the system is controlled by sliding mode. Based on solving linear matrix inequalities (LMI), we obtain the design method of sliding mode and controller. The sufficient conditions for the asymptotical stability of the sliding mode dynamics are given by using LMI technique and the Lyapunov stability theory, and it has been shown that the state trajectories can be driven onto the sliding surface in a finite time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theories.

    Mathematics Subject Classification: Primary: 93D05, 93D09; Secondary: 03F10.


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  • Figure 1.  Trajectory of state $ x_{1}(t) $ before adding controller

    Figure 2.  Trajectory of state $ x_{2}(t) $ before adding controller

    Figure 3.  control input signal

    Figure 4.  Trajectory of state $ x_{1}(t) $ after adding controller

    Figure 5.  Trajectory of state $ x_{2}(t) $ after adding controller

    Figure 6.  Trajectory of sliding mode variable

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