在本論文中我們將探討不確定多重時變時間延遲細胞神經網路(DCNN)、雙向聯想記憶神經網路(DBAMNN)及Cohen-Grossberg 神經網路(DCGNN)等三種網路之全域穩定性的研究。經由線性矩陣不等式法(LMI)，我們將提出一些與時間延遲相關及與延遲時間無關的判則，以保證系統之強韌穩定性。在這些延遲神經網路系統的回授矩陣與延遲回授矩陣中，我們探討三種不確定性參數的形式，包含有結構式擾動、非結構式擾動及區間擾動等。我們將由一些實際數值模擬例子來說明所獲結果的有效性，並驗證我們的結果優於近年來相關文獻的結果。

In this dissertation, we will investigate the global stability for some uncertain neural networks with multiple time-varying delays. These well-known neural networks include delayed cellular neural networks (DCNNs), delayed bidirectional associative memory neural networks (DBAMNNs), and delayed Cohen-Grossberg neural networks (DCGNNs). Delay-dependent and delay-independent criteria will be proposed to guarantee the robust stability of these uncertain delayed neural networks via linear matrix inequality (LMI) approach. Three types of uncertainties on feedback and delayed feedback matrices in these uncertain delayed neural networks will be considered in this study, namely uncertainties with structured perturbation, norm-bounded unstructured perturbation, and interval perturbation. Some numerical examples will be given to illustrate the effectiveness of our results. Some comparisions are made to show that our results are better than some results in recent literature.

誌謝……………………………………………………………………………………i
摘要……………………………………………………………………...................... iv
ABSTRACT…………………………………………………….……….................. v
NOMENCLATURE………………………………………………...…………….. vi
LIST OF ABBREVIATIONS……………………………………………..……vii
LIST OF FIGURES AND TABLES…………………………………..……… viii
CHAPTER 1 INTRODUCTION……………………………………………... 1
1.1 Motivation………….……..…………………………………….. 1
1.2 Brief Sketch of the Contents……………...…………………….. 4
CHAPTER 2 MATHEMATICAL PRELIMINARIES……………………. 7
2.1 Some Definitions………………...……………………………… 7
2.2 Preliminary Lemmas………………...………………………….. 9
CHAPTER 3 DELAYED CELLULAR NEURAL NETWORKS……. 10
3.1 Basic Concepts of Cellular Neural Networks………...………... 10
3.2 GES for Uncertain Cellular Neural Networks with Multiple
Time-varying Delays via LMI Approach………..………….... 16
3.3 An Illustrative Example…..……………………….…………… 29
CHAPTER 4 INTERVAL DELAYED NEURAL NETWORKS………. 31
4.1 Introduction……………..…………………………………….. 31
4.2 GES and GAS for Interval Delayed Neural Networks with Multiple Time-varying Delays via LMI Approach………….... 31
4.3 Illustrative Examples……………...…………………………… 41
CHAPTER 5 BIDIRECTIONAL ASSOCIATIVE MEMORY
NEURAL NETWORKS…………………………………….. 45
5.1 Introduction……………………..…………………………….. 45
5.2 GES for Uncertain Delayed BAM Neural Networks with
Multiple Time-varying Delays via LMI Approach……..…...… 48
5.3 Illustrative Examples………………..……………..………..…. 65
CHAPTER 6 COHEN-GROSSBERG NEURAL NETWORKS……… 71
6.1 Introduction…………...……………………………………….. 71
6.2 GAS for Uncertain Delayed Cohen-Grossberg Neural Networks
with Multiple Time-varying Delays via LMI Approach…..….. 74
6.3 Illustrative Examples……………………...…………………… 85
CHAPTER 7 CONCLUSION AND DISCUSSION……………………... 88
REFERENCES……………………………………………………………………. 91

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