A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays

Abstract

In this Letter, the analysis problem for the existence and stability of periodic solutions is investigated for a class of general discrete-time recurrent neural networks with time-varying delays. For the neural networks under study, a generalized activation function is considered, and the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. By employing the latest free-weighting matrix method, an appropriate Lyapunov-Krasovskii functional is constructed and several sufficient conditions are established to ensure the existence, uniqueness, and globally exponential stability of the periodic solution for the addressed neural network. The conditions are dependent on both the lower bound and upper bound of the time-varying time delays. Furthermore, the conditions are expressed in terms of the linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Two simulation examples are given to show the effectiveness and less conservatism of the proposed criteria.

Self-excitation of neurons leads to multiperiodicity of discrete-time neural networks with distributed delays

“…When k (n) ≡ 0, system (13) has a unique equilibrium Σ which is located in each B Σ and exponentially stable in H Σ . Obviously, our results either improve or extend existing ones [13,14,21,22]. [5-7, 9, 13, 14, 16, 19-21].…”

“…For such dynamical behavior, we can refer to Figure 2 (the initial condition is set to be the circle with center (0, 0) and radius 1). When we change system parameters into (14) becomes an autonomous discrete-time neural system [13,21,22]. By Corollary 3.2, there exists a unique equilibrium in B Σ which is exponentially stable in each H Σ .…”

Improved delay-dependent stability analysis for uncertain stochastic neural networks with time-varying delay

“…Therefore, the stability of delayed neural networks has aroused considerable interests in recent years, since the dynamic behavior of neural network often involves time delays, which may bring the instability of systems, see e.g. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and references therein. In these literatures, stability results can be classified into two types: delay-independent stability criteria and delay-dependent stability criteria.…”

Global robust exponential stability of discrete-time interval BAM neural networks with time-varying delays

“…However, when implementing 0307-904X/$ -see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.apm.2008.01.019 the continuous-time neural network for computer simulation, for experimental or computational purposes, it is essential to formulate a discrete-time system that is an analogue of the continuous-time neural network [19]. Generally speaking, the stability analysis of continuous-time neural networks is not applicable to the discrete version [20].…”