Direct quaternion method-based stability criteria for quaternion-valued Takagi-Sugeno fuzzy BAM delayed neural networks using quaternion-valued Wirtinger-based integral inequality

R. Sriraman; P. Vignesh; V. C. Amritha; G. Rachakit; Prasanalakshmi Balaji; R. Sriraman; P. Vignesh; V. C. Amritha; G. Rachakit; Prasanalakshmi Balaji

doi:10.3934/math.2023532

AIMS Mathematics

2023, Volume 8, Issue 5: 10486-10512. doi: 10.3934/math.2023532

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Direct quaternion method-based stability criteria for quaternion-valued Takagi-Sugeno fuzzy BAM delayed neural networks using quaternion-valued Wirtinger-based integral inequality

1.
Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu-603 203, India
2.
Department of Mathematics, Mepco Schlenk Engineering College, Tamil Nadu-626 005, India
3.
Department of Mathematics, National Institute of Technology Warangal, Telangana-506004, India
4.
Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai-52290, Thailand
5.
Department of Computer Science, King Khalid University, Abha-62529, Saudi Arabia

Received: 01 January 2023 Revised: 12 February 2023 Accepted: 17 February 2023 Published: 01 March 2023
MSC : 92B20, 93D05, 93D20, 03E72, 47S05

This paper investigates the global asymptotic stability problem for a class of quaternion-valued Takagi-Sugeno fuzzy BAM neural networks with time-varying delays. By applying Takagi-Sugeno fuzzy models, we first consider a general form of quaternion-valued Takagi-Sugeno fuzzy BAM neural networks with time-varying delays. Then, we apply the Cauchy-Schwarz algorithm and homeomorphism principle to obtain sufficient conditions for the existence and uniqueness of the equilibrium point. By utilizing suitable Lyapunov-Krasovskii functionals and newly developed quaternion-valued Wirtinger-based integral inequality, some sufficient criteria are obtained to guarantee the global asymptotic stability of the considered networks. Further, the results of this paper are presented in the form of quaternion-valued linear matrix inequalities, which can be solved using the MATLAB YALMIP toolbox. Two numerical examples are presented with their simulations to demonstrate the validity of the theoretical analysis.
- global asymptotic stability,
- quaternion-valued neural networks,
- Lyapunov-Krasovskii functional,
- Takagi-Sugeno fuzzy,
- time-varying delays
Citation: R. Sriraman, P. Vignesh, V. C. Amritha, G. Rachakit, Prasanalakshmi Balaji. Direct quaternion method-based stability criteria for quaternion-valued Takagi-Sugeno fuzzy BAM delayed neural networks using quaternion-valued Wirtinger-based integral inequality[J]. AIMS Mathematics, 2023, 8(5): 10486-10512. doi: 10.3934/math.2023532

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Abstract

This paper investigates the global asymptotic stability problem for a class of quaternion-valued Takagi-Sugeno fuzzy BAM neural networks with time-varying delays. By applying Takagi-Sugeno fuzzy models, we first consider a general form of quaternion-valued Takagi-Sugeno fuzzy BAM neural networks with time-varying delays. Then, we apply the Cauchy-Schwarz algorithm and homeomorphism principle to obtain sufficient conditions for the existence and uniqueness of the equilibrium point. By utilizing suitable Lyapunov-Krasovskii functionals and newly developed quaternion-valued Wirtinger-based integral inequality, some sufficient criteria are obtained to guarantee the global asymptotic stability of the considered networks. Further, the results of this paper are presented in the form of quaternion-valued linear matrix inequalities, which can be solved using the MATLAB YALMIP toolbox. Two numerical examples are presented with their simulations to demonstrate the validity of the theoretical analysis.

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