Non-separation method-based global stability criteria for Takagi-Sugeno fuzzy quaternion-valued BAM delayed neural networks using quaternion-valued auxiliary function-based integral inequality

This paper examines the global asymptotic stability of Takagi-Sugeno fuzzy quaternion-valued BAM neural networks with discrete, distributed and leakage delays using non-separation method. By applying Takagi-Sugeno fuzzy models , we first consider a general form of Takagi-Sugeno fuzzy quaternion-valued BAM neural networks with time delays. Then, we apply the Cauchy-Schwarz algorithm and homeomorphism principle in order to establish the existence and uniqueness of the equilibrium point. By using appropriate Lyapunov-Krasovskii functionals and quaternion-valued auxiliary function-based integral inequality, we derive new delay-dependent global asymptotic stability conditions for the considered neural networks. Furthermore, we present our results in terms of quaternion-valued linear matrix inequalities that can be solved in the MATLAB YALMIP toolbox. To demonstrate the validity of the theoretical analysis, we provide two numerical evaluations with simulations.