Discrete-Time Stochastic Quaternion-Valued Neural Networks with Time Delays: An Asymptotic Stability Analysis

Symmetry

Grienggrai Rajchakit¹  Rajendran Samidurai²  Ramalingam Sriraman³  CheePeng Lim⁴  Pharunyou Chanthorn⁵ 

[1] Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand;Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu-632115, India;Department of Science and Humanities, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Avadi, Tamil Nadu-600 062, India;Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds, VIC 3216, Australia;Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand;

关键词: stochastic disturbances;    quaternion-valued neural networks;    real-imaginary separation method;    Lyapunov fractional;    linear matrix inequality;   

DOI  :  10.3390/sym12060936

来源: DOAJ

【 摘 要 】

Stochastic disturbances often cause undesirable characteristics in real-world system modeling. As a result, investigations on stochastic disturbances in neural network (NN) modeling are important. In this study, stochastic disturbances are considered for the formulation of a new class of NN models; i.e., the discrete-time stochastic quaternion-valued neural networks (DSQVNNs). In addition, the mean-square asymptotic stability issue in DSQVNNs is studied. Firstly, we decompose the original DSQVNN model into four real-valued models using the real-imaginary separation method, in order to avoid difficulties caused by non-commutative quaternion multiplication. Secondly, some new sufficient conditions for the mean-square asymptotic stability criterion with respect to the considered DSQVNN model are obtained via the linear matrix inequality (LMI) approach, based on the Lyapunov functional and stochastic analysis. Finally, examples are presented to ascertain the usefulness of the obtained theoretical results.

【 授权许可】

Unknown