強健正向系統的穩定度分析與控制器設計

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姓名

李宗庭(Tsung-Ting Li) 查詢紙本館藏

畢業系所

電機工程學系

論文名稱

強健正向系統的穩定度分析與控制器設計
(Stability Analysis and Controller Design for Robust Positive Systems)

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摘要(中)

本論文係研究正向系統之穩定性分析及穩定化控制設計，研究的範疇包含連續時間與離散時間兩大系統，系統中含有的區間跟凸形不確定量因子，是本文的主要探討之列。針對穩定性與正向性分析問題，而推導出新的充份與必要條件，基於此條件，搭配狀態迴授來設計控制器，便可應用於控制系統的穩定化設計上。利用前述之分析結果，配合線性歸劃方法來尋找控制器參數。最後以實際的正向系統為例，對此系統設計控制器，討論補償前與補償後系統性能的差異，經由模擬結果顯示，所設計的控制器是有效且適用的。

摘要(英)

This thesis is concerned with stability and stabilization of interval and polytopic systems with the positivity constraints. Both continuous-time and discrete-time are discussed. For stability analysis and stabilization problems of those systems, we derive some new conditions. Then based on these conditions, a linear programming method is applied to design controllers. Several examples, including compartmental systems and Leslie systems are given to demonstrate the effectiveness and applicability of the proposed methods.

關鍵字(中)

★ 線性歸劃
★ 狀態迴授
★ 正向系統

關鍵字(英)

★ positive systems
★ linear programming
★ state feedback

論文目次

Contents I
List of Figures V
List of Tables VII
Chapter 1 Introductions 1
1.1 Motivations and Literature reviews 1
1.2 Organization 2
Chapter 2 Notations and Preliminaries 4
2.1 Notations 4
2.2 Positive Linear Systems 5
2.2.1 Continuous-time Positive Linear Systems 5
2.2.2 Discrete-time Positive Linear Systems 6
2.3 Metzler matrix 7
2.4 Asymptotically Stability 7
2.5 Lyapunov’s Direct Method 8
2.6 Summary 9
Chapter 3 Stability Analysis and Controller Design of Continuous-time Interval and Polytopic Systems under Positivity Constraint 10
3.1 Stability Analysis and Controller Design of Continuous-time Interval Systems under Positivity Constraint 10
3.1.1 Stability Analysis of Continuous-time Interval Linear Systems under Positivity Constraint 11
3.1.2 Controller Design of Continuous-time Interval Linear Systems under Positivity Constraint 14
3.2 Stability Analysis and Controller Design of Continuous-time Polytopic Systems under Positivity Constraint 17
3.2.1 Stability Analysis of Continuous-time Polytopic Linear Systems under Positivity Constraint 17
3.2.2 Controller Design of Continuous-time Polytopic Linear Systems under Positivity Constraint 20
3.3 Illustrative Examples 28
3.4 Summary 38
Chapter 4 Stability Analysis and Controller Design of Discrete-time Interval and Polytopic Systems under Positivity Constraint 39
4.1 Stability Analysis and Controller Design of Discrete-time Interval Systems under Positivity Constraint 39
4.1.1 Stability Analysis of Discrete-time Interval Linear Systems under Positivity Constraint 39
4.1.2 Controller Design of Discrete-time Interval Linear Systems under Positivity Constraint 43
4.2 Stability Analysis and Controller Design of Discrete-time Polytopic Systems under Positivity Constraint 46
4.2.1 Stability Analysis of Discrete-time Polytopic Linear Systems under Positivity Constraint 46
4.2.2 Controller Design of Discrete-time Polytopic Linear Systems under Positivity Constraint 50
4.3 Illustrative Examples 57
4.4 Summary 67
Chapter 5 Stabilization Problems on Compartmental Systems and Leslie Systems 68
5.1 Stabilization Problem on Compartmental Systems 68
5.1.1 Overview of Compartmental Systems 68
5.1.2 Stabilization of Compartmental Systems 69
5.2 Stabilization Problem on Leslie Systems 73
5.2.1 Overview of Leslie Systems 73
5.2.2 Stabilization of Leslie Systems 74
5.3 Summary 78
Chapter 6 Conclusions 79
References 80
Appendix 86
Publication List 103

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指導教授

莊堯棠(Yau-Tang Juang)

審核日期

2011-7-7

推文