姓名吳岱儒(Day-Ru Wu) 查詢紙本館藏 畢業系所電機工程學系 論文名稱時延系統穩定度分析

(Analysis of Time-Delay Systems)檔案[Endnote RIS 格式] [Bibtex 格式] [檢視] [下載]

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摘要(中)本論文主要針對具有時延系統的問題作進一步之研究。由於時間延遲將會改變系統的特徵方程式，因此研究方法將用來分析討論改變後的系統特徵方程式是否穩定。一般來說，當我們在檢查系統的穩定性時，若是利用延遲無關的穩定準則來測試時，可以相當簡單容易的討論，但如果利用延遲相關的穩定性準則時，通常需要比較複雜難處理的程序。由於延遲無關準則比延遲相關準則較保守，所以本論文將採用延遲相關準則來研究時延系統。

主要的研究方法將採用複變函數理論來處理由於時間延遲而改變的系統特徵方程式，然後輔以電腦軟體來分析，以發展出新的研究方法來決定時延系統的穩定性，由於以往所研究出的穩定準則所求出最大的可允許延遲區間皆從零開始，本論文的研究方法所求出的延遲區間並不一定要從零開始，而且或許有些系統可以得到一個以上的多個延遲區間使得系統在這些穩定延遲區間裡面仍具有穩定的狀態。因此應用同樣的特性來研究具有比例型時間延遲因子的時延系統，並且探討α穩定度之時延系統。摘要(英)In this thesis, stability of linear time-invariant time-delay systems is considered. An imaginary axis intersection sequence of delay times is decided. Then some necessary and sufficient conditions for stability are derived. Therefore, the maximum delay time interval is obtained. In addition, the multiple delay time intervals allowed may be determined. And using the scheme proposed in this thesis, some examples reveal that time-delay systems stability is not necessary that the allowable delay time must vary from zero. In the sequel, stability of linear time-invariant systems with multiple time delays is considered. Finally, linear time- delay systems with decay rate that is dependent on the delay is studied. Some examples are provided to illustrate the merits of the proposed method. 關鍵字(中)★ 比例型延遲

★ 時間延遲

★ 漸近穩定度

★ 延遲區間關鍵字(英)★ time delay

★ asymptotic stability

★ delay interval

★ Commensurate delays

★ decay rate論文目次ABSTRACT i

LIST OF FIGURES ii

CHAPTER 1 Introduction 1

1.1Motivation 1

1.2Literature Survey 2

1.3Organization of this thesis 3

CHAPTER 2 Delay Time Intervals for Stability of Time-Delay Systems 4

2.1 Introduction 4

2.2 Problem Formulation 5

2.3 Main Results 5

2.4 Examples 8

2.5 Conclusions 12

Chapter 3 Stability of Linear Time-Invariant System with Commensurate Delays 19

3.1 Introduction 19

3.2 Problem Formulation 20

3.3 Main Results 21

3.4 Examples 25

3.5 Conclusions 27

Chapter 4 Stability of Time-Delay Systems with the Decay Rate 35

4.1 Introduction 35

4.2 Problem Formulation 36

4.3 Main Results 36

4.4 Examples 41

4.5 Conclusions 45

Chapter 5 Conclusions and Future Research 51

List of Figures

Fig 2.1: The graph in (2.6) for Example 2.1 13

Fig 2.2: The plot with for Example 2.1 13

Fig 2.3: The plot with for Example 2.2 14

Fig 2.4: The graph in (2.6) for Example 2.3 14

Fig 2.5: The plot with for Example 2.3 15 Fig 2.6: The plot with for Example 2.3 15

Fig 2.7: State trajectories with time delay for Example 2.3 16

Fig 2.8: The graph in (2.6) for Example 2.4 16

Fig 2.9: The plot with for Example 2.4 17

Fig 2.10: The plot with for Example 2.4 17

Fig 2.11:State trajectories with time delay for Example 2.4 18

Fig 2.12:State trajectories with time delay for Example 2.4 18

Fig 3.1:The graph in (3.6) for Example 3.1 28

Fig 3.2: The plot with for Example 3.1 28

Fig 3.3: The plot with for Example 3.1 29

Fig 3.4: State trajectories with time delay for Example 3.1 29

Fig 3.5: State trajectories with time delay for Example 3.1 30

Fig 3.6: State trajectories with time delay for Example 3.1 30

Fig 3.7: The graph in (3.6) for Example 3.2 31

Fig 3.8: The plot with for Example 3.2 31

Fig 3.9: The plot with for Example 3.2 32

Fig 3.10:State trajectories with time delay for Example 3.2 32

Fig 3.11:State trajectories with time delay for Example 3.2 33

Fig 3.12:State trajectories with time delay for Example 3.2 33

Fig 3.13:State trajectories with time delay for Example 3.2 34

Figure 4.1: The contour D 46

Figure 4.2: The plot with and decay rate for Example 4.1 46

Figure 4.3: The plot with and decay rate for Example 4.2 47

Figure 4.4: The plot with and decay rate for Example 4.2 47

Figure 4.5: The plot with and decay rate for Example 4.3 48

Figure 4.6: The plot with and decay rate for Example 4.3 48

Figure 4.7: The plot with and decay rate for Example 4.4 49

Figure 4.8: The plot with and decay rate for Example 4.4 49

Figure 4.9: The plot with and decay rate for Example 4.5 50

Figure 4.10:The plot with and decay rate for Example 4.5 50參考文獻[1] J. Chiasson, “A method for computing the interval of the delay values for which a differential-delay system is stable,” IEEE Transactions on Automatic Control, Vol. 33, 1176-1178, 1988.

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