^{1,2}

^{1,3}

^{1,2}

^{1}

^{2}

^{3}

The global asymptotic robust stability of equilibrium is considered for neutral-type hybrid bidirectional associative memory neural networks with time-varying delays and parameters uncertainties. The results we obtained in this paper are delay-derivative-dependent and establish various relationships between the network parameters only. Therefore, the results of this paper are applicable to a larger class of neural networks and can be easily verified when compared with the previously reported literature results. Two numerical examples are illustrated to verify our results.

Stability analysis of neural networks is an issue of both theoretical and practical importance due to the fact that in some applications the designed neural network is required to have a unique and stable equilibrium point [

It is well known that a series of neural networks related to bidirectional associative memory (BAM) models have been proposed by Kosko [

Moreover, due to the complicated dynamic properties of the neural cells in the real world, the existing neural network models in many cases cannot characterize the properties of a neural reaction process precisely. It is natural and important that systems will contain some information about the derivative of the past state to further describe and model the dynamics for such complex neural reactions [

However, the existing stability results [

Motivated by the preceding discussion, in this paper, we are going to deal with the problem of global asymptotic robust stability for neutral-type hybrid bidirectional associative memory neural networks with time-varying delays and parameters uncertainties. By constructing a novel Lyapunov functional, novel delay-derivative-dependent criteria are derived. Finally, two examples are provided to demonstrate the effectiveness of the obtained results.

Throughout this paper, we will use the following notations: let

The three commonly used matrix norms

For the vector

Dynamical behavior of a neutral-type hybrid BAM neural network with time-varying delays is described by the following set of differential equations:

It will be assumed that

for all

The activation functions satisfy the following properties.

There exist some positive constants

for all

There exist positive constants

Assume that

Then, the transformed system is as follows:

It can be verified that the functions

By assumption (H2) and the above equations, we can have

In this paper, we will assume that the norms of the matrices

For

For

For

For

For any two vectors

Note that the equilibrium point of system (

For given scalars

Define the following positive definite Lyapunov functional:

The derivative of

We can write the following inequalities as follows:

Combining (

Let

By Fact 1,

Clearly,

The stability results presented [

Choosing

For given scalars

By setting

Let the activation functions satisfy assumptions (H2) and (H3) and let the network parameters satisfy (

Assume that there are no neutral terms and the system of BAM neural networks is described as

Define the following positive definite Lyapunov functional:

Following the similar line of the proof of Theorem

For given scalars

We will now give the following examples to demonstrate the applicability and advantages of our results.

Assume that the network parameters of neural system (

Then we obtain

Since

For the sufficiently small values of

The four required conditions for stability are

In what follows, we consider a special model in this example and give simulation results for the sake of verification of our proposed results. We choose

Trajectories of

Assume that the network parameters of neural system (

By Lemmas

Since

Thus we have

Let

For the neural network parameters given in Example

Trajectories of

In this paper, we have obtained new sufficient conditions for the global asymptotic robust stability of the equilibrium point for the class of neutral-type hybrid bidirectional associative memory neural networks with time-varying delays and parameters uncertainties. Some new delay-derivative-dependent stability criteria are derived to ascertain the global asymptotic stability of the BAM neural networks. To obtain less conservative stability criterion, some new upper bound norms for the interconnection matrices of the neural networks are used. The obtained results can be easily verified as they can be expressed in terms of the network parameters only. Two illustrative examples are given to show the effectiveness of the proposed results.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by National Natural Science Foundation of China (no. 61103211) and Postdoctoral Science Foundation of Chongqing (no. XM201310).