Discrete-time BAM neural networks with variable delays

Abstract

This Letter deals with the global exponential stability of discrete-time bidirectional associative memory (BAM) neural networks with variable delays. Using a Lyapunov functional, and linear matrix inequality techniques (LMI), we derive a new delay-dependent exponential stability criterion for BAM neural networks with variable delays. As this criterion has no extra constraints on the variable delay functions, it can be applied to quite general BAM neural networks with a broad range of time delay functions. It is also easy to use in practice. An example is provided to illustrate the theoretical development.

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

“…Recently, many researchers have studied stability properties of the neural networks and presented various sufficient conditions for the asymptotic or exponential stability of the BAM neural networks [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Lou and Cui [7] studied the global asymptotic stability of delayed BAM neural networks with impulses by constructing suitable Lyapunov functional and using matrix theory.…”

“…Therefore, it is important to study the dynamics of discrete-time neural networks. In recent years, the dynamical behaviors of various discrete-time neural networks have been studied in [10][11][12][19][20][21][22][23][24]. Mohamad [10] considered the global exponential stability of the continuous-time BAM neural network and its discrete analogue by using the method of Lyapunov functional.…”

“…Liao and Wong [5] derived some sufficient conditions for the global robust asymptotic stability of the continuous-time interval BAM neural networks. Liu et al [12] discussed the global exponential stability of the discrete-time BAM neural networks by means of a Lyapunov functional and inequality techniques. However, the authors did not consider the robust stability for discrete-time BAM neural networks in [12].…”

“…Liu et al [12] discussed the global exponential stability of the discrete-time BAM neural networks by means of a Lyapunov functional and inequality techniques. However, the authors did not consider the robust stability for discrete-time BAM neural networks in [12]. To the best of our knowledge, the robust exponential stability for the discrete-time interval BAM neural networks with time-varying delays has never been tackled.…”

New Improved Exponential Stability Criteria for Discrete-Time Neural Networks with Time-Varying Delay

“…And they can ideally keep the dynamic characteristics, functional similarity, and even the physical or biological reality of the continuous-time networks under mild restriction. Thus, the stability analysis problems for discrete-time neural networks have received more and more interest, and some stability criteria have been proposed in literature see [14][15][16][17][18][19][20][21][22][23][24][25] . In 14 , Liu et al researched a class of discrete-time RNNs with time-varying delay, and proposed a delay-dependent condition guaranteeing the global exponential stability.…”