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Continuous Stability TS Fuzzy Systems Novel Frame Controlled by a Discrete Approach and Based on SOS Methodology

Author

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  • Ameni Ellouze

    (Control & Energy Management Laboratory (CEM-Lab), National Engineering School of Sfax, University of Sfax, Sfax 3038, Tunisia
    Higher Institute of Computer Science and Multimedia of Gabès (ISIMG), University of Gabès, Gabès 6033, Tunisia)

  • Omar Kahouli

    (Department of Electronics Engineering, Community College, University of Ha’il, Ha’il 81481, Saudi Arabia)

  • Mohamed Ksantini

    (Control & Energy Management Laboratory (CEM-Lab), National Engineering School of Sfax, University of Sfax, Sfax 3038, Tunisia)

  • Ali Rebhi

    (Department of Electronics Engineering, Community College, University of Ha’il, Ha’il 81481, Saudi Arabia)

  • Nidhal Hnaien

    (Laboratory of Thermal Processes, Research and Technology Centre of Energy, Hammam Lif 2050, Tunisia)

  • François Delmotte

    (Laboratory of Computer Engineering and Automation of Artois, University of Artois, Technoparc Futura, 62400 Bethune, France)

Abstract

Generally, the continuous and discrete TS fuzzy systems’ control is studied independently. Unlike the discrete systems, stability results for the continuous systems suffer from conservatism because it is still quite difficult to apply non-quadratic Lyapunov functions, something which is much easier for the discrete systems. In this paper and in order to obtain new results for the continuous case, we proposed to connect the continuous with the discrete cases and then check the stability of the continuous TS fuzzy systems by means of the discrete design approach. To this end, a novel frame was proposed using the sum of square approach (SOS) to check the stability of the continuous Takagi Sugeno (TS) fuzzy models based on the discrete controller. Indeed, the control of the continuous TS fuzzy models is ensured by the discrete gains obtained from the Euler discrete form and based on the non-quadratic Lyapunov function. The simulation examples applied for various models, by modifying the order of the Euler discrete fuzzy system, are presented to show the effectiveness of the proposed methodology.

Suggested Citation

  • Ameni Ellouze & Omar Kahouli & Mohamed Ksantini & Ali Rebhi & Nidhal Hnaien & François Delmotte, 2021. "Continuous Stability TS Fuzzy Systems Novel Frame Controlled by a Discrete Approach and Based on SOS Methodology," Mathematics, MDPI, vol. 9(23), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3129-:d:695061
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    Cited by:

    1. Artun Sel & Bilgehan Sel & Umit Coskun & Cosku Kasnakoglu, 2022. "SOS-Based Nonlinear Observer Design for Simultaneous State and Disturbance Estimation Designed for a PMSM Model," Sustainability, MDPI, vol. 14(17), pages 1-12, August.

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