Dissipativity and passivity analysis for discrete-time complex-valued neural networks with time-varying delay

Abstract

In this paper, we consider the problem of dissipativity and passivity analysis for complex-valued discrete-time neural networks with time-varying delays. The neural network under consideration is subject to time-varying. Based on an appropriate Lyapunov-Krasovskii functional and by using the latest free-weighting matrix method, a sufficient condition is established to ensure that the neural networks under consideration is strictly (, , )-dissipative. The derived conditions are presented in terms of linear matrix inequalities. A numerical example is presented to illustrate the effectiveness of the proposed results.

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.…”

“…Besides that, the dissipativity theory offers a critical methodology for designing control systems through an input-output representation using system energy-related contemplations. 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].…”