Dissipativity Analysis of Complex-Valued Stochastic Neural Networks With Time-Varying Delays

Abstract

This paper considers the dissipativity analysis problem for complex-valued stochastic neural networks (CVSNNs) with time-varying delays. By constructing the Lyapunov functions, using Jensen inequality and stochastic analysis techniques, several sufficient conditions for the exponential dissipativity and (Q, R, S)-dissipativity in the mean square are obtained in terms of linear matrix inequalities (LMIs). Compared with the existing ones, in our work, some results which are more applicable for CVSNNs with time-varying delays case are derived. Finally, two numerical examples are provided to illustrate the effectiveness and improvement of our theoretical results. INDEX TERMS Complex-valued stochastic neural network, time-varying delays, dissipativity, Itô formula.

Robust Dissipativity Analysis of Hopfield-Type Complex-Valued Neural Networks with Time-Varying Delays and Linear Fractional Uncertainties

“…Similar to the publications in [31,34,35,37], the energy supply function for the NN model in (5) is defined as…”

“…We notice from the available publications that a number of definitions for strictly (Q, S, R)-dissipativity [27,30], global exponential disspativity and global dissipativity [31,33] are provided in the Euclidean space R n . These definitions have been extended in recent publication [31,[34][35][36][37] to the complex plane C n .…”

“…Remark 5. In recent years, dynamical analysis with respect to various CVNN models has been conducted [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][31][32][33][34][35][36][37]. In this regard, the research interest pertaining to HTCVNN models has increased significantly in recent years [1,13,[16][17][18].…”

“…The MATLAB software package is used to solve the LMIs effectively. We devise a number of numerical models and their empirical results positively ascertain the obtained results.Mathematics 2020, 8, 595 2 of 22 models has been highly focused, resulting in many research studies with comprehensive results [26][27][28][29][30][31][32][33][34][35][36][37][38][39]. On the other hand, it is important to investigate the stability of NN models with the effects of linear fractional uncertainties.…”

“…As a result, many publications on the dissipativity analysis of NN models are available in the literature [26][27][28][29][30][31][32][33][34][35][36][37]40]. As an example, a number of new conditions with respect to the (Q, S, R) dissipativity criteria, global exponential dissipativity, and global dissipativity have been developed for a class of CVNN models in [31,37]. In [32], the use of Dini derivative concepts has resulted in novel sufficient conditions for the dissipativity of complex-valued bi-directional associative memory NN models.…”