System decomposition method-based global stability criteria for T-S fuzzy Clifford-valued delayed neural networks with impulses and leakage term

Abdulaziz M. Alanazi; R. Sriraman; R. Gurusamy; S. Athithan; P. Vignesh; Zaid Bassfar; Adel R. Alharbi; Amer Aljaedi; Abdulaziz M. Alanazi; R. Sriraman; R. Gurusamy; S. Athithan; P. Vignesh; Zaid Bassfar; Adel R. Alharbi; Amer Aljaedi

doi:10.3934/math.2023774

AIMS Mathematics

2023, Volume 8, Issue 7: 15166-15188. doi: 10.3934/math.2023774

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System decomposition method-based global stability criteria for T-S fuzzy Clifford-valued delayed neural networks with impulses and leakage term

1.
Department of Mathematics, University of Tabuk, Tabuk-71491, Saudi Arabia
2.
Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chengalpattu, Tamil Nadu-603 203, India
3.
Department of Mathematics, Mepco Schlenk Engineering College, Tamil Nadu-626 005, India
4.
Department of Information Technology, University of Tabuk, Tabuk-71491, Saudi Arabia
5.
College of Computing and Information Technology, University of Tabuk, Tabuk-71491, Saudi Arabia

Received: 10 February 2023 Revised: 12 April 2023 Accepted: 16 April 2023 Published: 24 April 2023
MSC : 92B20, 93D05, 93D20, 37H30, 03E72

This paper investigates the global asymptotic stability problem for a class of Takagi-Sugeno fuzzy Clifford-valued delayed neural networks with impulsive effects and leakage delays using the system decomposition method. By applying Takagi-Sugeno fuzzy theory, we first consider a general form of Takagi-Sugeno fuzzy Clifford-valued delayed neural networks. Then, we decompose the considered $ n $-dimensional Clifford-valued systems into $ 2^mn $-dimensional real-valued systems in order to avoid the inconvenience caused by the non-commutativity of the multiplication of Clifford numbers. By using Lyapunov-Krasovskii functionals and integral inequalities, we derive new sufficient criteria to guarantee the global asymptotic stability for the considered neural networks. Further, the results of this paper are presented in terms of real-valued linear matrix inequalities, which can be directly solved using the MATLAB LMI toolbox. Finally, a numerical example is provided with their simulations to demonstrate the validity of the theoretical analysis.
- global asymptotic stability,
- Clifford-valued neural networks,
- Lyapunov-Krasovskii functionals,
- Takagi-Sugeno fuzzy,
- impulses
Citation: Abdulaziz M. Alanazi, R. Sriraman, R. Gurusamy, S. Athithan, P. Vignesh, Zaid Bassfar, Adel R. Alharbi, Amer Aljaedi. System decomposition method-based global stability criteria for T-S fuzzy Clifford-valued delayed neural networks with impulses and leakage term[J]. AIMS Mathematics, 2023, 8(7): 15166-15188. doi: 10.3934/math.2023774

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Abstract

This paper investigates the global asymptotic stability problem for a class of Takagi-Sugeno fuzzy Clifford-valued delayed neural networks with impulsive effects and leakage delays using the system decomposition method. By applying Takagi-Sugeno fuzzy theory, we first consider a general form of Takagi-Sugeno fuzzy Clifford-valued delayed neural networks. Then, we decompose the considered $ n $-dimensional Clifford-valued systems into $ 2^mn $-dimensional real-valued systems in order to avoid the inconvenience caused by the non-commutativity of the multiplication of Clifford numbers. By using Lyapunov-Krasovskii functionals and integral inequalities, we derive new sufficient criteria to guarantee the global asymptotic stability for the considered neural networks. Further, the results of this paper are presented in terms of real-valued linear matrix inequalities, which can be directly solved using the MATLAB LMI toolbox. Finally, a numerical example is provided with their simulations to demonstrate the validity of the theoretical analysis.

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