臺灣博碩士論文加值系統

本論文針對時變區間獨立與分佈式延遲中性不確定性遞迴類神經網路提出強健穩定度分析與狀態估測器問題的探討，其中時變延遲是在一已知區間。穩定度分析的部分，是針對獨立式與分佈式時變延遲不確定性的中性類神經網路探討全域性的強健時延穩定度分析。其中，激勵函數被假定為有界且全域性利普希茨（Lipschitz）連續。藉由李阿普諾夫函數（Lyapunov function）法和線性矩陣不等式（Linear matrix inequality）技巧，具有獨立式與分佈式時變延遲不確定性的中性類神經網路的穩定度準則會被建立並以線性矩陣不等式表示。在設計狀態估測器方面，藉由李阿普諾夫方法（Lyapunov method）和線性矩陣不等式（Linear matrix inequality）技巧建構狀態估測器的充分條件，滿足誤差狀態系統之全域漸近穩定。並且會證實存在的條件及所要設計的估測器以線性矩陣不等式來表示並解之。最後，一些數值範例證明上述所提理論的可應用性及有效性。

This thesis presents the complete study of stability analysis and state estimators design. The system is focused on neutral neural networks with both interval discrete and distributed time-varying delays, where the time-varying delays are in a given range. In a stability analysis problem, the purpose is to develop globally robust delay-dependent stability for neutral uncertain neural networks with both discrete and distributed delays. The activation functions are supposed to be bounded and globally Lipschitz continuous. By using a Lyapunov function approach and linear matrix inequality (LMI) techniques, the stability criteria for the neutral uncertain neural networks with both discrete and distributed delays are established in the form of LMIs, which can be readily verified by using standard numerical software. In an estimator design problem, the estimation for neutral neural network with both discrete and distributed interval time-varying delays is investigated. By using the Lyapunov-Krasovskii method, a linear matrix inequality (LMI) approach is developed to construct sufficient conditions for the existence of admissible state estimators such that the error-state system is globally asymptotically stable. Then, we show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. Finally, some illustrative examples have been presented to demonstrate the effectiveness of the proposed approach.

Contents
中文摘要.......I
Abstract......II
Acknowledgment ......III
Contents........V
List of Tables.......VII
List of Figures.....VIII
Chapter 1 Introduction.............1
1.1 Neural Networks................1
1.2 Linear Matrix Inequalities (LMIs)......5
1.3 Time delay systems..............13
1.4 Delay-Independent/Delay-Dependent Conditions.......15
1.5 Contribution of the Thesis......16
1.6 Brief Sketch of the Contents..........17
Chapter 2 Delay-Dependent Robust Uncertain Stabilization for Uncertain Neutral Recurrent Neural Networks with Interval Time-varying Discrete and Distributed Delays.............................18
2.1 Introduction.........................18
2.2 Problem formulation..............21
2.3 Mathematical formulation......24
2.4 Examples...............................36
2.5 Summary...............................39
Chapter 3 Delay-Dependent Exponential State Estimator Design for Neutral Recurrent Neural Networks with Interval Time-varying Discrete and Distributed Delays.......40
3.1 Introduction.........................40
3.2 Problem formulation...............42
3.3 Mathematical formulation......46
3.4 Examples...............................57
3.5 Summary..............................62
Chapter 4 Conclusions and Future Research..........63
4.1 Conclusions....................63
4.2 Further Research Directions..............63
References.......65
Biography.................76
List of Tables
Table2.1 The derivatives of the delays.............38
Table3.1 The upper bound cases of the derivatives of the delays......59
List of Figures
Fig.1.1 Biological neuron model.........1
Fig.1.2 neuron model.................2
Fig.1.3 Neural network architectures.....3
Fig.1.4 Multi-layer perceptron with one hidden layer.......4
Fig.1.5 Feed-forward network block diagram................4
Fig.1.6 Single input and output with time delay.........13

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