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Student Number 87324046 Author Day-Ru Wu(§d©§¾§) Author's Email Address No Public. Statistics This thesis had been viewed 2337 times. Download 1314 times. Department Electrical Engineering Year 1999 Semester 2 Degree Master Type of Document Master's Thesis Language zh-TW.Big5 Chinese Title Analysis of Time-Delay Systems Date of Defense 2000-07-04 Page Count 58 Keyword asymptotic stability Commensurate delays decay rate delay interval time delay Abstract 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. Table of Content 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

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