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研究生：	盧建余 Lu, Chien-Yu
論文名稱：	使用線性矩陣不等式法探討時延系統的強健控制 Robust Control of Time-Delay Systems: A Linear Matrix Inequality Approach
指導教授：	蔡聖鴻 Tsai, S. H. Jason
學位類別：	博士 Doctor
系所名稱：	電機資訊學院 - 電機工程學系 Department of Electrical Engineering
論文出版年：	2004
畢業學年度：	92
語文別：	英文
論文頁數：	160
中文關鍵詞：	線性矩陣不等式、穩定度、時延系統、濾波器、控制器
外文關鍵詞：	stability, controller, filtering, time-delay systems, linear matrix inequality
相關次數：	點閱：96 下載：2
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　　本論文旨在使用線性矩陣不等式法探討強健時延系統控制。其研究主題包括針對一系列不確定性時延系統、二維離散狀態延遲蘿莎模式、隨機時延系統及中性型隨機時延系統探討其穩定性、控制器設計、濾波器設計及追蹤控制設計。在穩定性分析方面，藉由狀態轉移矩陣法，我們提出創新的穩定法則。根據Lyapunov-Krasovskii 法及結合線性矩陣不等式法，可推得簡單且改善時延相關的穩定法則。濾波器設計方面，提出一種新的濾波器設計方法，使得時延系統達到穩定且同時能滿足狀的強健性能指標。追蹤控制方面，針對時延系統，藉由線性矩陣不等式法設計一種強健追蹤器以保証閉迴路的追蹤能滿足的性能指標。至於二維離散狀態延遲系統方面，則提出一種強健的二維動態控制器，使得閉迴路穩定同時滿足的性能指標。在隨機時延系統控制方面，以線性矩陣不等式推衍而得到的時延相關控制器亦被設計出，最後本論文亦提出中性型隨機線性與非線性系統的強健穩定化控制器。

　　A complete study of the robust control of time-delay systems via the linear matrix inequality approach is presented in this dissertation. This includes the developments of the stability analysis/controller design/filtering problem/tracking control for a series of uncertain systems with time delay, two-dimensional (2-D) discrete state-delayed systems described by Roesser model, a class of stochastic systems with time delay and a class of neutral stochastic systems. A novel state transformation matrix has been proposed for the stability analysis. Based on the Lyapunov-Krasovskii functionals combining with linear matrix inequality (LMI) techniques, simple and improved delay-dependent robust stability criteria are derived. For the filtering design, asymptotically stabilizing Kalman filtering and filtering approaches are presented for the system with time delay. For the robust tracking control, the proposed tracker obtained in terms of LMIs guarantees the stability of closed-loop systems and makes the output to approach the command reference input with a specified performance. For the two-dimensional discrete state-delayed system, a 2-D dynamic output feedback controller is designed to achieve the closed-loop system asymptotic stability and a specified performance using the LMI approach. Also, we develop a 2-D filtering approach with a specified performance measure. For the stochastic system with time delay, a state feedback controller is designed to guarantee the closed-loop system remaining stable for all admissible uncertainties. Finally, we propose a state feedback controller to stabilize the class of neutral stochastic nonlinear systems with a specified performance.

Abstract	ii
Acknowledgement	iii
Contents	iv
List of Figures	vii

Chapter 1 Introduction	1
1.1	Time-Delay Systems	                        1
1.2	Delay-Independent/Delay-Dependent Conditions	4
1.3	Mathematical Modelling	                        5   
1.4	Linear Matrix Inequality (LMI)	               11
1.5	Contribution of the Dissertation	       15
1.6	Brief Sketch of the Contents	               16
Chapter 2 Robust Stability and Robust Stabilization for 
          Systems with Time Delay	               17                                                                                                                             
2.1 Introduction	                               17
2.2 Delay-Dependent Stability	                       18
2.2.1 System Description	                       19
2.2.2 Main Results	                               20
2.2.3 Examples	                                       26
2.3 Delay-Dependent Stabilization	               29
2.3.1 Preliminaries	                               29
2.3.2 Main Results	                               30
2.3.3 Examples	                                       33
2.4 Stability of Cellular Neural Networks with
    Time-Varying Delay	                               35
     2.4.1 Model of Cellular Neural Networks with 
           Delay (DCNNs)	                       35
     2.4.2 Existence of the Equilibrium and Stability 
           of DCNNs	                               36 
     2.4.3 Examples	                               38
2.5 Summary	                                       39
Chapter 3 Robust Filtering for a Class of Uncertain
          Interval Systems with Time Delay	       40
3.1 Introduction	                               40
3.2 Robust Filtering for Delay-Dependent 
    Interval Systems	                               41
3.2.1 Problem Formulation and Assumptions	       42
3.2.2 Main Results	                               45
3.2.3 An Illustrative Example	                       51
3.3 Delay-Dependent Robust Filtering for 
    Interval Systems with State Delays	               54
3.3.1 Problem Formulation and Assumptions	       54
3.3.2 Main Results	                               56
3.3.3 An Illustrative Example	                       63
3.4 Summary	                                       64
Chapter 4 Robust Tracking for Systems with Time Delay  65
4.1 Introduction	                               65
4.2 Delay-Dependent Robust Tracking for Uncertain
    Continuous Time-Delay Systems	               66
4.2.1 System Description	                       66
4.2.2 Main Results	                               69
4.2.3 An Illustrative Example	                       76
4.3 Robust   Tracking for Discrete Time-Delay Systems  78
4.3.1 System Description	                       78
4.3.2 Main Results	                               81
4.3.3 An Illustrative Example	                       87
4.4 Summary	                                       89
Chapter 5 Two-Dimensional Robust Stabilization for
          State-Delayed Systems	                       90
5.1 Introduction	                               90
5.2 Preliminaries	                               91
5.3 Main Results	                               92
5.4 An Illustrative Example	                      104
5.5 Summary	                                      106
Chapter 6 Two-Dimensional Robust   Filtering for 
          State-Delayed Systems	                      107
6.1 Introduction	                              107
6.2 Preliminaries	                              108
6.3 Main Results	                              109
6.4 An Illustrative Example	                      117
6.5 Summary	                                      118
Chapter 7 Robust Stabilization of Uncertain 
          Stochastic Systems	                      119
7.1 Introduction	                              119
7.2 An LMI-Based Approach for Robust Stabilization of 
    Uncertain Stochastic Systems with 
    Time-Varying Delays	                              120 
7.2.1 Preliminaries	                              120
7.2.2 Main Results	                              122
7.2.3 An Illustrative Example	                      126
7.3 Robust Stabilization of Uncertain 
    Stochastic Neutral Interval Systems with 
    Multiple Delays	                              127
    7.3.1 Preliminaries	                              127
     7.3.2 Main Results                      	      129
     7.3.3 Examples	                              136
7.4 Delay-Dependent Robust  Control for Nonlinear 
    Stochastic Neutral Systems with State Delays      138
     7.4.1 Preliminaries	                      138
     7.4.2 Main Results	                              139
     7.4.3 An Illustrative Example	              146
7.5 Summary	                                      148
Chapter 8 Conclusions	                              149
References	                                      152
Biography	                                      160
                                    

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