Abstract
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.
Highlights
The research on dynamical behavior analysis for neural network (NN) models has attracted increasing attention in recent years and their results have been widely used in a variety of science and engineering disciplines [1,2,3,4,5,6,7,8,9]
The investigation on discrete-time stochastic quaternion-valued neural networks (DSQVNNs) models with time delays and their mean-square asymptotic stability analysis is novel, which constitutes the main contribution of our paper
(2) Unlike the traditional stability analysis, we establish new mean-square asymptotic stability criteria for the considered DSQVNN models, which is achieved through the Lyapunov functional and real-imaginary separate-type activation functions
Summary
The research on dynamical behavior analysis for NN models has attracted increasing attention in recent years and their results have been widely used in a variety of science and engineering disciplines [1,2,3,4,5,6,7,8,9]. Several researchers have studied various dynamical behaviors of discrete-time NN models. Several aspects of SNN models have been analysed extensively in both continuous and discrete-time cases; e.g., the problems of passivity [40], robust stability [41], exponential stability [42], robust dissipativity [44], mean-square exponential input-to-state stability [49], and mean-square exponential input-to-state stability for QVNNs [50]. The investigation on DSQVNN models with time delays and their mean-square asymptotic stability analysis is novel, which constitutes the main contribution of our paper. (2) Unlike the traditional stability analysis, we establish new mean-square asymptotic stability criteria for the considered DSQVNN models, which is achieved through the Lyapunov functional and real-imaginary separate-type activation functions.
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