Stability and Stabilization of TS Fuzzy Systems via Line Integral Lyapunov Fuzzy Function
Abstract
:1. Introduction
2. Mathematical Tools and Preliminaries
2.1. Structure of TS Multi-Model
2.2. Mean Value Theorem
2.3. Line Integral Lyapunov Function
2.4. SFS Method
2.4.1. Diffusion Process
2.4.2. First Updating Process
2.4.3. Second Updating Process
Algorithm 1 SFS algorithm |
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3. Stability Analysis
3.1. Analysis with Quadratic Functions
3.2. Analysis with Non-Quadratic Stability Functions
4. Stabilization
5. Simulation Example
6. Conclusions and Future Works
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Meredef, I.e.; Hammoudi, M.Y.; Betka, A.; Hamiane, M.; Mimoune, K. Stability and Stabilization of TS Fuzzy Systems via Line Integral Lyapunov Fuzzy Function. Electronics 2022, 11, 3136. https://doi.org/10.3390/electronics11193136
Meredef Ie, Hammoudi MY, Betka A, Hamiane M, Mimoune K. Stability and Stabilization of TS Fuzzy Systems via Line Integral Lyapunov Fuzzy Function. Electronics. 2022; 11(19):3136. https://doi.org/10.3390/electronics11193136
Chicago/Turabian StyleMeredef, Imad eddine, Mohamed Yacine Hammoudi, Abir Betka, Madina Hamiane, and Khalida Mimoune. 2022. "Stability and Stabilization of TS Fuzzy Systems via Line Integral Lyapunov Fuzzy Function" Electronics 11, no. 19: 3136. https://doi.org/10.3390/electronics11193136