臺灣博碩士論文加值系統

本論文探討時間延遲切換系統之穩定性分析與切換法則設計。在時間延遲切換系統中有兩種切換方式，一為時間切換；另一為狀態切換。探討在兩種切換方式下，得到穩定的切換法則，進行時間延遲切換系統之穩定性分析。
在時間切換方式中，是依據狀態變數的響應，求出停留在穩定的獨立切換系統的總時間與停留在不穩定的獨立切換系統的總時間之比值，以保證其整個時間延遲切換系統是穩定的，其研究結果並導出與時間延遲有關及與時間延遲無關的穩定條件。此外，研究結果與方法可延伸應用到具未確定量的時間延遲切換系統與時間延遲大型切換系統中。
在狀態切換方式中，運用李亞普諾夫穩定定理，使得系統在所設計的切換法則下為穩定，並導出其穩定條件。時間延遲切換系統之穩定性分析中，本論文依與時間延遲有關及與時間延遲無關分別導出時間延遲切換系統之穩定條件。在研究中得到一個重要的結果，若時間延遲切換系統其每一個獨立系統皆為不穩定的系統時，在所設計的切換法則下，滿足穩定的條件時，系統的響應為漸進穩定。另外，研究結果與方法可延伸應用到時間延遲大型切換系統中。

This dissertation attempts to investigate the stability and switching law design of time-delay switched systems. Two approaches are used to construct the switching laws for the stability analysis of time-delay switched systems. One is the time-driven switching method; the other is state-driven.
The time-driven switching method is that the total activation time ratio of stable individual systems to unstable individual systems will be determined via the state solution. The sufficient stability conditions with delay-independent criteria and delay-dependent criteria have been derived. Besides, this method and results can be extended to uncertain time-delay switched systems and time-delay large-scale switched systems.
The state-driven switching method uses Lyapunov stability theorem to construct a state-driven switching strategy such that the time-delay switched system is asymptotically stable. The sufficient stability conditions with delay-independent criteria and delay-dependent criteria have been derived. In particular, the present results demonstrated that this approach can be adopted even when individual systems are all unstable. Moreover, this method and results can be extended to time-delay large-scale switched systems.

Abstract(Chinese) i
Abstract(English) ii
Acknowledgment(Chinese) iii
Contents iv
List of Figures vii
Chapter 1. Introduction 1
1.1 Motivation and background 1
1.2 Review of previous research 3
1.3 Main task and organization of this dissertation 6
Chapter 2. Time-delay switched systems 9
2.1 System description and problem statement 9
2.1.1 Time-delay switched systems 12
2.1.2 Interval time-delay switched systems 13
2.1.3 Uncertain time-delay switched systems 14
2.1.4 Time-delay large-scale switched systems 15
2.2 Problem statement 16
Chapter 3. Stability analysis and switching law design with the time-
driven switching method 18
3.1 On delay-independent analysis of time-delay switched
systems 18
3.1.1 Stability analysis and switching law design 18
3.1.2 Numeric example 23
3.1.3 Summary 24
3.2 On delay-dependent analysis of time-delay switched systems
25
3.2.1 Stability analysis and switching law design 25
3.2.2 Numeric example 31
3.2.3 Summary 34
3.3 On delay-independent analysis of interval time-delay
switched systems 34
3.3.1 Stability analysis and switching law design 35
3.3.2 Numeric example 39
3.3.3 Summary 41
3.4 On delay-dependent analysis of interval time-delay
switched systems 42
3.4.1 Stability analysis and switching law design 42
3.4.2 Numeric example 48
3.4.3 Summary 49
3.5 On delay-independent analysis of uncertain time-delay
switched systems 50
3.5.1 Stability analysis and switching law design 50
3.5.2 Numeric example 54
3.5.3 Summary 56
3.6 On delay-dependent analysis of uncertain time-delay
switched systems 56
3.6.1 Stability analysis and switching law design 56
3.6.2 Numeric example 60
3.6.3 Summary 62
3.7 On delay-independent analysis of time-delay large-scale
switched systems 62
3.7.1 Stability analysis and switching law design 63
3.7.2 Numeric example 68
3.7.3 Summary 72
3.8 On delay-dependent analysis of time-delay large-scale
switched systems 72
3.8.1 Stability analysis and switching law design 73
3.8.2 Numeric example 79
3.8.3 Summary 83
Chapter 4. Stability analysis and switching law design with the
state-driven switching method 84
4.1 On delay-independent analysis of time-delay switched
systems 84
4.1.1 Stability analysis and switching law design 85
4.1.2 Numeric example 99
4.1.3 Summary 106
4.2 On delay-independent analysis of time-delay switched
systems with LMIs approach 106
4.2.1 Stability analysis and switching law design 107
4.2.2 Numeric example 114
4.2.3 Summary 119
4.3 On delay-dependent analysis of time-delay switched systems 120
4.3.1 Stability analysis and switching law design 120
4.3.2 Numeric example 130
4.3.3 Summary 136
4.4 On delay-independent analysis of time-delay large-scale
switched systems 137
4.4.1 Stability analysis and switching law design 137
4.4.2 Numeric example 150
4.4.3 Summary 156
Chapter 5. Stability analysis and synthesis of switched discrete-
time systems 158
5.1 Analysis and Synthesis of switched discrete-time systems 158
5.1.1 Stability analysis and switching law design 158
5.1.2 Numeric example 168
5.1.3 Summary 176
5.2 On delay-independent analysis of time-delay switched
discrete-time systems 176
5.2.1 Stability analysis and switching law design 177
5.2.2 Numeric example 182
5.2.3 Summary 186
5.3 Analysis and Synthesis of large-scale switched discrete-
time systems 186
5.3.1 Stability analysis and switching law design 187
5.3.2 Numeric example 191
5.3.3 Summary 200
Chapter 6. Conclusions and future works 202
6.1 Conclusions 202
6.2 Future works 204
References 205
Biography 213

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