On the boundedness of solutions of some fuzzy dynamical control systems

Omar Kahouli; Amina Turki; Mohamed Ksantini; Mohamed Ali Hammami; Ali Aloui; Omar Kahouli; Amina Turki; Mohamed Ksantini; Mohamed Ali Hammami; Ali Aloui

doi:10.3934/math.2024257

AIMS Mathematics

2024, Volume 9, Issue 3: 5330-5348. doi: 10.3934/math.2024257

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On the boundedness of solutions of some fuzzy dynamical control systems

1.
Department of Electronics Engineering, Applied College, University of Hail, Hail 2440, Saudi Arabia
2.
Control and Energies Management Laboratory (CEM-Lab), National Engineering School of Sfax, University of Sfax, Tunisia
3.
Tunisia Faculty of Sciences of Sfax, Department of Mathematics, University of Sfax, Tunisia

Received: 05 December 2023 Revised: 11 January 2024 Accepted: 16 January 2024 Published: 26 January 2024
MSC : 93C10, 93C42, 93D15

The asymptotic behavior of solutions of fuzzy control systems is a component of the study of fuzzy control theory. The study of stability for T-S (Takagi-Sugeno) fuzzy systems, which process qualitative data through linguistic expressions, is the subject of this paper. Asymptotic stability is conservative in many real-world applications due to measurement noise and other disruptions. The ultimate limit, which indicates that the mistakes stay in a specific area close to the origin after a long enough amount of time, is a crucial characteristic that is frequently defined for such systems. We are interested with the problem of the state feedback controller for T-S fuzzy models with uncertainties where the global exponential ultimate boundedness of solutions is studied for certain fuzzy control systems. We use common quadratic Lyapunov function and parallel distributed compensation controller techniques to study the asymptotic behavior of the solutions of fuzzy control system in presence of perturbations. An example demonstrating the validity of the main result is discussed.
- fuzzy systems,
- uncertainties,
- boundedness of solutions,
- convergence and stability
Citation: Omar Kahouli, Amina Turki, Mohamed Ksantini, Mohamed Ali Hammami, Ali Aloui. On the boundedness of solutions of some fuzzy dynamical control systems[J]. AIMS Mathematics, 2024, 9(3): 5330-5348. doi: 10.3934/math.2024257

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Abstract

The asymptotic behavior of solutions of fuzzy control systems is a component of the study of fuzzy control theory. The study of stability for T-S (Takagi-Sugeno) fuzzy systems, which process qualitative data through linguistic expressions, is the subject of this paper. Asymptotic stability is conservative in many real-world applications due to measurement noise and other disruptions. The ultimate limit, which indicates that the mistakes stay in a specific area close to the origin after a long enough amount of time, is a crucial characteristic that is frequently defined for such systems. We are interested with the problem of the state feedback controller for T-S fuzzy models with uncertainties where the global exponential ultimate boundedness of solutions is studied for certain fuzzy control systems. We use common quadratic Lyapunov function and parallel distributed compensation controller techniques to study the asymptotic behavior of the solutions of fuzzy control system in presence of perturbations. An example demonstrating the validity of the main result is discussed.

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