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This paper deals with the problem of delay-dependent stability criterion of uncertain periodic switched recurrent neural networks with time-varying delays. When uncertain discrete-time recurrent neural network is a periodic system, it is expressed as switched neural network for the finite switching state. Based on the switched quadratic Lyapunov functional approach (SQLF) and free-weighting matrix approach (FWM), some linear matrix inequality criteria are found to guarantee the delay-dependent asymptotical stability of these systems. Two examples illustrate the exactness of the proposed criteria.

Recurrent neural networks (RNNs) are a very important tool for many application areas such as associative memory, pattern recognition, signal processing, model identification, and combinatorial optimization. With the development of research on RNNs in theory and application, the model is more and more complex. When the continuous-time RNNs are simulated using computer, they should be discretized into discrete-time RNNs [

In most literatures it is required that parameter uncertainty matrices, such as

The dynamic behaviors of those models are foundations for applications. Under (

Motivated by the above discussions, the authors intend to study a problem of the delay-dependent stability criterion of uncertain discrete-time recurrent neural networks with time-varying delays that the uncertain recurrent neural networks have a finite number of sub-RNNs, and the sub-RNNs may change from one to another according to arbitrary switching and restricted switching. The contributions of this paper are the following. (1) Using a switching graph, uncertain periodic recurrent neural networks with time-varying delays are transformed into switched recurrent neural networks; (2) the derivative of the SQLF (

This paper is organized as follows. In Section

In many electronic circuits, nonmonotonic functions can be more appropriate to describe the neuron activation in designing and implementing an artificial neural network [

For any

Under the assumption, the equilibrium points of UDNN (

Let

When

Throughout this paper, the superscript

Let

Suppose that

We consider the following SQLF:

It is clear that the following equations are true:

Firstly, we prove that under

In order to strictly guarantee

In addition, for any semipositive definite matrix

Similar to the conclusion in [

Then we add the terms on the right side of (

And

Secondly, based on the switching graph

Using the method in [

In

Combined with Theorem

Let

Consider the discrete-time recurrent neural network (

Employing the LMIs in Theorem

Allowable upper bound of

0 | 2 | 4 | 6 | 8 | 20 | |

Theorem | 9 | 11 | 13 | 15 | 17 | 29 |

Global convergence of states

Consider the discrete-time recurrent neural network (

Employing the LMIs in [

Allowable upper bound of

0 | 2 | 4 | 6 | 8 | 10 | 20 | |

Reference [ | 20 | 22 | 24 | 26 | 28 | 30 | 40 |

Corollary | 38 | 40 | 42 | 44 | 46 | 48 | 58 |

Allowable upper bound of

0 | 2 | 4 | 6 | 10 | |

Reference [ | 11 | 13 | 15 | 17 | 21 |

Corollary | 12 | 14 | 16 | 18 | 22 |

Global convergence of states

Employing the LMIs in [

This paper was dedicated to the delay-dependent stability of uncertain periodic switched recurrent neural networks with time-varying delay. A less conservative LMI-based globally stability criterion is obtained with the switched quadratic Lyapunov functional approach and free-weighting matrix approach for periodic uncertain discrete-time recurrent neural networks with a time-varying delay. One example illustrates the exactness of the proposed criterion. Another example demonstrates that the proposed method is an improvement over the existing one.

This work was supported by the Sichuan Science and Technology Department under Grant 2011JY0114. The authors would like to thank the Associate Editor and the anonymous reviewers for their detailed comments and valuable suggestions which greatly contributed to this paper.