CLC number: TP183

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Received: 2003-10-08

Revision Accepted: 2003-12-05

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ZHANG Sen-lin, LIU Mei-qin. LMI-based approach for global asymptotic stability analysis of continuous BAM neural networks[J]. Journal of Zhejiang University Science A, 2005, 6(1): 32~37.

@article{title="LMI-based approach for global asymptotic stability analysis of continuous BAM neural networks",

author="ZHANG Sen-lin, LIU Mei-qin",

journal="Journal of Zhejiang University Science A",

volume="6",

number="1",

pages="32~37",

year="2005",

publisher="Zhejiang University Press & Springer",

doi="10.1631/jzus.2005.A0032"

}

%0 Journal Article

%T LMI-based approach for global asymptotic stability analysis of continuous BAM neural networks

%A ZHANG Sen-lin

%A LIU Mei-qin

%J Journal of Zhejiang University SCIENCE A

%V 6

%N 1

%P 32~37

%@ 1673-565X

%D 2005

%I Zhejiang University Press & Springer

%DOI 10.1631/jzus.2005.A0032

TY - JOUR

T1 - LMI-based approach for global asymptotic stability analysis of continuous BAM neural networks

A1 - ZHANG Sen-lin

A1 - LIU Mei-qin

J0 - Journal of Zhejiang University Science A

VL - 6

IS - 1

SP - 32

EP - 37

%@ 1673-565X

Y1 - 2005

PB - Zhejiang University Press & Springer

ER -

DOI - 10.1631/jzus.2005.A0032

**Abstract: **Studies on the stability of the equilibrium points of continuous bidirectional associative memory (BAM) neural network have yielded many useful results. A novel neural network model called standard neural network model (SNNM) is advanced. By using state affine transformation, the BAM neural networks were converted to SNNMs. Some sufficient conditions for the global asymptotic stability of continuous BAM neural networks were derived from studies on the SNNMs’ stability. These conditions were formulated as easily verifiable linear matrix inequalities (LMIs), whose conservativeness is relatively low. The approach proposed extends the known stability results, and can also be applied to other forms of recurrent neural networks (RNNs).

**
**

. INTRODUCTION

. STATEMENT OF PROBLEMS

Let

In this paper, we assume that the training of continuous BAM neural network is finished before we analyze it. Thus, the weights are not changeable in the process of stability analysis. Because there are many detailed discussions on the existence and uniqueness of the equilibrium points of BAM neural networks (Xu et al.,

. STANDARD NEURAL NETWORK MODEL

If

The unique equilibrium point of SNNM Eq.(

The derivative of

The sector conditions,

Although the proof in Theorem 1 is similar to that of the book (Boyd et al.,

. STABILITY ANALYSIS

If

Taking the affine transformation

System Eq.(

Let

According to Eq.(

The proof of Lemma 1 can be referred to the proof of the Lemma 1 in the paper of Barabanov and Prokhorov (

Therefore, system Eq.(

Here, we summarize the steps of our approach for stability analysis of the continuous BAM neural network Eq.(

1. The continuous BAM neural network Eq.(

2. It is necessary to find an equilibrium point

3. The state vector should be shifted in such a way that the equilibrium point of system Eq.(

4. For each transformed transfer function [which has a form

5. The MATLAB LMI Toolbox (Gahinet et al.,

. AN EXAMPLE

The connection weights of system Eq.(

. CONCLUSION AND FUTURE DIRECTIONS

restricted to the sector condition. For particular activation functions (e.g. tanh), however, we could mitigate the conservatism for the stable conditions by using their other properties (e.g. restricted slope). It is another direction we will research in future.

* Project (No. 60074008) supported by the National Natural Science Foundation of China

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