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Keywords = non-Sugeno integral inequalities

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29 pages, 608 KiB  
Article
Novel Fuzzy Ostrowski Integral Inequalities for Convex Fuzzy-Valued Mappings over a Harmonic Convex Set: Extending Real-Valued Intervals Without the Sugeno Integrals
by Mesfer H. Alqahtani, Der-Chyuan Lou, Fahad Sikander, Yaser Saber and Cheng-Chi Lee
Mathematics 2024, 12(22), 3495; https://doi.org/10.3390/math12223495 - 8 Nov 2024
Viewed by 918
Abstract
This study presents new fuzzy adaptations of Ostrowski’s integral inequalities through a novel class of convex fuzzy-valued mappings defined over a harmonic convex set, avoiding the use of the Sugeno integral. These innovative inequalities generalize the recently developed interval forms of real-valued Ostrowski [...] Read more.
This study presents new fuzzy adaptations of Ostrowski’s integral inequalities through a novel class of convex fuzzy-valued mappings defined over a harmonic convex set, avoiding the use of the Sugeno integral. These innovative inequalities generalize the recently developed interval forms of real-valued Ostrowski inequalities. Their formulations incorporate integrability concepts for fuzzy-valued mappings (FVMs), applying the Kaleva integral and a Kulisch–Miranker fuzzy order relation. The fuzzy order relation is constructed via a level-wise approach based on the Kulisch–Miranker order within the fuzzy number space. Additionally, numerical examples illustrate the effectiveness and significance of the proposed theoretical model. Various applications are explored using different means, and some complex cases are derived. Full article
(This article belongs to the Special Issue Novel Approaches in Fuzzy Sets and Metric Spaces)
20 pages, 6534 KiB  
Article
Observer-Based Controller Using Line Integral Lyapunov Fuzzy Function for TS Fuzzy Systems: Application to Induction Motors
by Rabiaa Houili, Mohamed Yacine Hammoudi, Mohamed Benbouzid and Abdennacer Titaouine
Machines 2023, 11(3), 374; https://doi.org/10.3390/machines11030374 - 10 Mar 2023
Cited by 2 | Viewed by 2118
Abstract
This paper deals with the stabilization problem of a nonlinear system described by a Takagi–Sugeno fuzzy (TSF) model with unmeasurable premise variables via a robust controller. Applying the sector nonlinearity techniques, the nonlinear system is represented by a decoupled fuzzy model. Then, we [...] Read more.
This paper deals with the stabilization problem of a nonlinear system described by a Takagi–Sugeno fuzzy (TSF) model with unmeasurable premise variables via a robust controller. Applying the sector nonlinearity techniques, the nonlinear system is represented by a decoupled fuzzy model. Then, we design a robust observer-based controller for the obtained fuzzy system by utilizing the differential mean value approach. The observer and controller gains are obtained by the separation principle, in which the problem is solved in the sum of linear matrix inequalities (LMIs). The paper presents two main contributions: A state feedback controller is designed using differential mean value (DMVT) which ensures robust stabilization of the nonlinear system. Additionally, the Luenberger observer is extended to the Takagi–Sugeno fuzzy models. The second contribution is to reduce conservatism in the obtained conditions, a non-quadratic Lyapunov function (known as the line integral Lyapunov fuzzy candidate (LILF)) is employed. Two examples are provided to further illustrate the efficiency and robustness of the proposed approach; specifically, the Takagi–Sugeno fuzzy descriptor of an induction motor is derived and a robust observer-based controller applied to the original nonlinear system. Full article
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15 pages, 1190 KiB  
Article
Stability and Stabilization of TS Fuzzy Systems via Line Integral Lyapunov Fuzzy Function
by Imad eddine Meredef, Mohamed Yacine Hammoudi, Abir Betka, Madina Hamiane and Khalida Mimoune
Electronics 2022, 11(19), 3136; https://doi.org/10.3390/electronics11193136 - 29 Sep 2022
Cited by 10 | Viewed by 2004
Abstract
This paper is concerned with the stability and stabilization problem of a Takagi-Sugeno fuzzy (TSF) system. Using a non-quadratic function (well-known integral Lyapunov fuzzy candidate (ILF)) and some lemmas, new sufficient conditions are established as linear matrix inequalities (LMIs), which are solved with [...] Read more.
This paper is concerned with the stability and stabilization problem of a Takagi-Sugeno fuzzy (TSF) system. Using a non-quadratic function (well-known integral Lyapunov fuzzy candidate (ILF)) and some lemmas, new sufficient conditions are established as linear matrix inequalities (LMIs), which are solved with a stochastic fractal search (SFS). The main advantage of the technique used is its small conservatives. Motivated by the mean value theorem, a state feedback controller based on a non-quadratic Lyapunov function is designed. Unlike other approaches based on poly-quadratic Lyapunov candidates, stability conditions of the closed loop are obtained in LMI regions. It is important to highlight that the time derivatives of membership functions do not appear in the used line integral Lyapunov function, which is the well-known problem of poly-quadratic Lyapunov functions. A numerical example is given to show the advantages and the utility of the integral Lyapunov fuzzy candidate, which provides a wider feasibility region than other Lyapunov functions. Full article
(This article belongs to the Section Systems & Control Engineering)
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