This paper deals with the stability problem for a class of impulsive neural networks. Some sufficient conditions which can guarantee the globally exponential stability of the addressed models with given convergence rate are derived by using Lyapunov function and impulsive analysis techniques. Finally, an example is given to show the effectiveness of the obtained results.

Recently, special interest has been devoted to the dynamics analysis of neural networks due to their potential applications in different areas of science. Particularly, there has been a significant development in the theory of neural networks with impulsive effects [

Let

Consider the following impulsive neural networks:

In this paper, we assume that some conditions are satisfied so that the equilibrium point of system (

(H_{0})

Furthermore, we will assume that the response function

(H_{1})

Note that _{1}), it holds that

Furthermore, let

To prove the stability of

In the following, the notion

Let

We introduce a definition as follows.

Assume

From the transformation

Furthermore, form the transformation

Given constant _{0}) and (H_{1}) are fulfilled; moreover, suppose that

We only need to prove

Consider the Lyapunov function as follows:

Then from conditions (H_{0})-(H_{1}) and (i), we get the upper right-hand derivative of

The proof of Theorem

Most of the existing results about the exponential stability of impulsive neural networks cannot effectively control the convergence rate. It is interesting to see that Theorem

In particular, if

Given constant _{0})-(H_{1}) are fulfilled; moreover, suppose that

there exists a constant

We only need to prove that

Consider the Lyapunov function as follows:

Then from conditions (H_{0})-(H_{1}) and (i), we get the upper right-hand derivative of

The proof of Theorem

Although Theorem

Given constant _{0})-(H_{1}) are fulfilled; moreover, suppose that

there exists a constant

We only need to prove that

Consider the Lyapunov functional as follows:

Then from conditions (H_{0})-(H_{1}) and (i), we get the upper right-hand derivative of

The proof of Theorem

The following illustrative example will demonstrate the effectiveness of our results.

Consider the following impulsive neural networks:

It is easy to see that _{1}) with

Let

This work was jointly supported by the Project of Shandong Province Higher Educational Science and Technology Program (J12LI04), Research Fund for Excellent Young and Middle-aged Scientists of Shandong Province (BS2012DX039), and National Natural Science Foundation of China (11226136, 11171192).