切換系統的穩定性分析與設計

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姓名

周均鴻(Jun-Hung Chou) 查詢紙本館藏

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電機工程學系

論文名稱

切換系統的穩定性分析與設計
(Stability analysis and design of switched systems)

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摘要(中)

摘要
切換系統為混成系統的一種，它由許多的子系統和一組切換訊號所構成。具polytope形式的切換系統和T-S模糊模型切換系統是本論文所探討的兩種切換系統。我們先對這兩種系統提出其為可穩定的充分條件，並且針對可穩定的系統提出穩定性的設計方法，而在設計的過程當中，遭遇到求解雙線性不等式的問題，因此，我們亦提出了以疊代線性不等式的演算法求解此類雙線性不等式的問題，並且各舉了兩個例子，說明我們所提出方法的存在價值與優點。

摘要(英)

Abstract
A switched system is a hybrid system that consists of several subsystems and a switching law indicating the active subsystem at each time instant. In this thesis, two categories of switched systems are considered. One is the switched system with polytopic uncertainties and the other is the switched T-S fuzzy system. Sufficient conditions are proposed for stabilizing the switched system with polytopic uncertainties and the switched T-S fuzzy system, respectively. The design methods are also proposed to stabilize these two switched systems. In design, we encounter the bilinear matrix inequalities (BLMIs) problem. An iterative linear matrix inequalities algorithm is proposed to solve the BLMI problems. Examples are given to illustrate the feasibility of the proposed results.

關鍵字(中)

★ 雙線性矩陣不等式
★ 切換系統
★ 線性矩陣不等式

關鍵字(英)

★ switched system
★ bilinear matrix inequality
★ linear matrix inequality

論文目次

CONTENTS
List of figures Ⅲ
CHAPTER 1 Introduction 1
1.1 Hybrid systems and switched systems 1
1.2 Organization 3
CHAPTER 2 Stability of Switched systems 5
2.1 Introduction 5
2.2 Stability under Arbitrary Switching 7
2.2.1 Common Lyapunov function 7
2.2.2 Matrices with commute pairwise property 8
2.2.3 Triangular system 11
2.2.4 Matrix pencil conditions 14
2.3 Stabilizing Switching Signals 16
2.3.1 A suitable switching signal 16
2.3.2 State-based switching strategy 25
2.3.3 Multiple Lyapunov Function 27
2.3.4 Slow switching 29
CHAPTER 3 T-S Fuzzy Model 32
3.1 Introduction to Takagi-Sugeno fuzzy model 32
3.2 Stability analysis via Lyapunov function 33
3.3 Parallel distributed compensation 34
3.4 Relaxed stability condition 35
CHAPTER 4 Stabilization of switched systems with polytopic uncertainties 37
4.1 Introduction 37
4.2 Preliminaries 38
4.2.1 Some definitions and lemmas 38
4.2.2 The uncertain systems of polytopic type 39
4.3 Two-switched uncertain system 41
4.4 Solution to the BLMI Problems 44
4.5 Multiple-switched uncertain system 45
4.6 Numerical Examples 47
4.7 Conclusions 52
CHAPTER 5 Stablilzation of switched T-S fuzzy system 53
5.1 Introduction 53
5.2 Problem statement 54
5.3 Two-switched T-S fuzzy system 56
5.4 Solution to the BLMI Problems 62
5.5 Multiple-switched T-S fuzzy system 64
5.6 Numerical Examples 66
5.7 Conclusions 75
CHAPTER 6 Conclusions and future works 76
6.1 Conclusions 76
6.2 Future works 77

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指導教授

莊堯棠(Yau-Tarng Juang)

審核日期

2005-6-30

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