應用投影法作受擾動奇異系統之強健性分析

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姓名

林慧玲(Hui-Ling Lin) 查詢紙本館藏

畢業系所

電機工程學系

論文名稱

應用投影法作受擾動奇異系統之強健性分析
(Robustness analysis of linear descriptor systems: utilizing projection method)

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摘要(中)

本論文中，主要是針對具參數不確定的連續和離散之奇異系統，做一個完整的分析研究。奇異系統優於狀態空間系統，可以很自然的描述一動態系統，故奇異系統廣泛地應用在電路、有界控制系統、電源系統、化學系統、經濟系統、生物學、機器人學、航空模型等其他領域。由於在實際的環境中，不管儀器再精密或是情況再理想，一定有不可避免的擾動或是參數變動的問題。所以，這些不確定因素的考量，是系統所不可或缺的。
本論文分別針對受擾動的連續和離散之奇異系統，提出投影法去求解受擾動系統穩定性分析的問題，並把結果延伸至分析奇異之延遲系統的強健穩定性，最後由給定的例子來證明我們的說法，並和先前文獻比較，得知我們的方法可以有效的降低系統保守性。
本論文的研究主要就是利用投影法，對上述的問題做一較完整的探討，我們期望能夠得到一個更精確的穩定準則。

摘要(英)

In this thesis, the robust stability of linear continuous-time, discrete-time and discrete state-delayed descriptor systems is investigated. Sufficient conditions are derived for ensuring that the mentioned linear descriptor systems remain asymptotically stable. The presented criteria in a complex LMI manner are checked by the projection method. The given numerical examples demostrate the validity and efficiency of the proposed method.

關鍵字(中)

★ 奇異系統
★ 強健控制

關鍵字(英)

★ singular systems
★ robust control

論文目次

CONTENTS
CHAPTER 1 Introduction .……….…………….….…………………….1
1.1 Motivation …………………………..…………………………….…….….1
1.2 Literature survey …………...………………………….……………………2
1.3 Organization of this thesis ……...……….…………….……………………2
CHAPTER 2 The projection scheme introduction .…………..……4
2.1 Introduction ……….………………………………………………………..4
2.2 The concept of the projection scheme …………………...…………………4
2.3 Projection operators for Hermitian matrices .….………………...…………5
2.4 Conclusions ………………………………….………………………...…10
CHAPTER 3 Robust stability analysis for uncertain
continuous and discrete descriptor systems …..…. 11
3.1 Introduction ………………………………………….……………………11
3.2 Problem formulation and preliminary ………..……….…………………..11
3.3 Robust stability analysis ……….…………………………….…………..13
3.4 Robustness analysis algorithm …………………………………………...17
3.5 Examples ……………………………………………….…………………19
3.6 Conclusions ………………………………………….……………………27
CHAPTER 4 Robust stability analysis for uncertain
discrete descriptor systems with state delay .…..28
4.1 Introduction …………………………………………………………….…28
4.2 Problem formulation and preliminary ………..……………………….…..28
4.3 Robust stability analysis …….………………………………….………..30
4.4 Robustness analysis algorithm …………………………………….……..33
4.5 Examples ……………………………………………….…………………34
4.6 Conclusions …………………………………………………….…………43
CHAPTER 5 Conclusions …………………………………….………44

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指導教授

莊堯棠(Yau-Tarng Juang)

審核日期

2003-6-10

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