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

Yuan Li; Ruxia Zhang; Yi Zhang; Bo Yang

doi:10.3934/naco.2020006

Article Contents

2020, Volume 10, Issue 3: 345-354. Doi: 10.3934/naco.2020006

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

School of science, Shenyang University of Technology, Shenyang, Liaoning 110870, China

^* Corresponding author: Ruxia Zhang
^* Corresponding author: Ruxia Zhang

Received: May 2019

Revised: August 2019

Published: June 2020

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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Abstract

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.

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

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

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

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Figure 3. control input signal

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

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

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Figure 6. Trajectory of sliding mode variable

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