本論文將探討不確定連續及離散多重時間延遲奇異擾動系統之強健穩定性問題。首先，考慮一類線性連續多重時間延遲奇異擾動系統之漸近穩定性；本文將提出一簡單的估測法則，來求得奇異擾動擾動參數 的上限值 ，以確保原系統在時為漸近穩定。此外，我們也將提出一種與 無關之延遲相關法則以確保系統之漸近穩定性。其次，本文將考慮不確定連續多重時間延遲奇異擾動系統之強健穩定性問題；我們將提出二種延遲相關法則，以確保不確定連續多重時間延遲奇異擾動系統，在有非結構化擾動存在時仍能保持其漸近穩定性。第三部份本文將討論一類不確定離散多重時間延遲系統之強健D穩定性。本文第四部份將討論當有結構化擾動及非結構化擾動存在時，不確定離散多重時間延遲奇異擾動系統之強健穩定性問題。我們將提出一些延遲相關或延遲無關法則，以確保不確定離散多重時間延遲奇異擾動系統之強健穩定性。本論文在相關議題所作之改進，將儘可能的與其他文獻之成果作比較；此外，本文也將提供一些數值例子來闡述我們之一些主要成果。

In this dissertation, the robust stability of uncertain continuous and discrete singularly perturbed systems with multiple time delays is investigated. Firstly, the asymptotic stability for a class of linear continuous singularly perturbed systems with multiple time delays is investigated. A simple estimate of an upper bound of singular perturbation parameter is proposed such that the original system is asymptotically stable for any . Moreover, a delay-dependent criterion, but -independent, is proposed to guarantee the asymptotic stability of the original system. Secondly, we consider the robust stability problem of uncertain continuous singularly perturbed systems with multiple time delays. Two delay-dependent criteria are proposed to guarantee the robust stability of a class of uncertain continuous multiple time-delay singularly perturbed systems subject to unstructured perturbations. Thirdly, the robust D-stability of nominally stable discrete uncertain systems with multiple time delays is considered. Finally, the robust stability of nominally stable uncertain discrete singularly perturbed systems with multiple time delays subject to unstructured and structured perturbations is investigated. Some criteria, delay-dependent or delay-independent, will be proposed to guarantee the robust stability of the uncertain discrete multiple time-delay singularly perturbed systems. The improvements of our results over those in recent literature are also illustrated if the comparisons are possible. Some numerical examples will also be provided to illustrate our main results.

CONTENTS
誌謝 iii
摘要 iv
ABSTRACT v
NOMENCLATURE vi
CHAPTER 1 INTRODUCTION 1

1.1 Motivation 1
1.2 Brief Sketch of the Contents 2

CHAPTER 2 MATHEMATICAL PRELIMINARIES 4

CHAPTER 3 ROBUST STABILITY OF UNCERTAIN CONTINUOUS SINGULARLY PERTURBED
SYSTEMS WITH MULTIPLE TIME DELAYS 7
3.1 Introduction 7
3.2 Stability for Singularly Perturbed Systems with Multiple Time Delays 10 10
3.3 Robust Stability for Uncertain Singularly Perturbed Systems with
Multiple Time Delays 24
3.4 Stability of Nominally Stable Uncertain Singularly Perturbed Systems
with Multiple Time Delays 39

CHAPTER 4 ROBUST STABILITY OF UNCERTAIN DISCRETE SINGULARLY PERTURBED
SYSTEMS WITH MULTIPLE TIME DELAYS 46
4.1 Introduction 46
4.2 D-Stability of Uncertain Discrete Systems with Multiple Time Delays 49
4.3 Robust Stability of Uncertain Discrete Time-Delay Singularly
Perturbed Systems with Unstructured Perturbations 59
4.3.1 Stability Criteria of Nominal Slow and Fast Subsystems 60
4.3.2 Stability Criteria of Uncertain Slow and Fast Subsystems 63
4.3.3 Stability Criteria of Uncertain System 67
4.4 Stability Bound of Uncertain Discrete Singularly Perturbed Systems
with Multiple Time Delays 76
4.4.1 Stability Criteria of Uncertain Slow and Fast Subsystems 76
4.4.2 Stability Bound of Uncertain System 79
4.5 Robust Stability of Uncertain Discrete Time-Delay Singularly
Perturbed Systems with Structured Perturbations 86
4.5.1 Stability Criteria of Nominal Slow and Fast Subsystems 86
4.5.2 Stability Criteria of Uncertain Slow and Fast Subsystems 87
4.5.3 Stability Criteria of Uncertain System 90

CHAPTER 5 CONCLUSIONS AND DISCUSSIONS 99

REFERENCES 106

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