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

Ameni Ellouze, Omar Kahouli, Mohamed Ksantini, Ali Rebhi, Nidhal Hnaien and François Delmotte
Additional contact information
Ameni Ellouze: Control & Energy Management Laboratory (CEM-Lab), National Engineering School of Sfax, University of Sfax, Sfax 3038, 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

Mathematics, 2021, vol. 9, issue 23, 1-18

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.

Keywords: discretization; continuous Takagi Sugeno (TS) fuzzy models; Euler approximation; non quadratic Lyapunov function; sum of square approach (SOS); polynomial Lyapunov function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/23/3129/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/23/3129/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:23:p:3129-:d:695061

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().