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研究生:陳堃峯
研究生(外文):Kun-Feng Chen
論文名稱:離散時間延遲系統之穩定性分析與迴授之穩定化設計
論文名稱(外文):Stability Analysis and Feedback Stabilization of Discrete-Time Delay Systems
指導教授:馮蟻剛
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:電機工程學研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2010
畢業學年度:98
語文別:英文
論文頁數:83
中文關鍵詞:離散系統時變狀態時間延遲線性矩陣不等式穩定性分析輸出迴授非線性擾動
外文關鍵詞:discrete-time systemtime-varying state delaylinear matrix inequalitystability analysisoutput-feedbackl nonlinear perturbation
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本論文主要使用線性矩陣不等式的方法研究離散時間延遲系統。研究主題包括具有時變之狀態時間延遲的離散系統、具有時變之狀態時間延遲與非線性擾動的離散系統,及具有時變之狀態間隔時間延遲的離散系統,探討其穩定性分析與輸出迴授穩定化設計。在穩定性分析方面,本論文提出一些以線性矩陣不等式表示的穩定性準則,且在推導穩定性準則的過程中引入新的自由權重矩陣,及使用最少的不等式,儘可能不使用會產生保守性的條件。在輸出迴授控制器的設計上,本論文提出一套以線性矩陣不等式作為條件的穩定化方法,不僅可容許較大的延遲範圍使得閉迴路延遲系統穩定,對於控制器增益尚可直接求得,以對控制器增益作適當的限制,這在實際工業應用上提供設計者相當大的便利性。最後,在數值範例的測試上,本論文所提的方法不僅可以得到較為不保守的條件,甚至對於一般文獻無法討論的穩定度系統也能夠適用。

This dissertation studies discrete-time systems with a time-varying state delay via the linear matrix inequality approach. The research includes the developments of delay- dependent stability analysis and output feedback stabilization for discrete-time systems with a time-varying state delay, discrete-time systems with a time-varying state delay and nonlinear perturbations, and discrete-time systems with an interval time-varying state delay. The derivations are based on the Lyapunov method and formulated by the linear matrix inequalities, which are convenient to solve. In the development of stability condi- tions, new free-weighting matrices are introduced, and the least number of inequalities are utilized, with the attempt to reduce as much conservatism as possible. In the proposed novel stabilizing output feedback controller design method, the gain matrix is a direct design variable, which offers great flexibility for the design purpose. To test the derived results, many numerical examples are adopted. Comparisons with results by existing methods indeed show that the proposed method is less conservative for the examples.

誌謝 i
摘要 ii
Abstract iii
Table of Contents iv
List of Tables vii
List of Figures viii
Notations ix
Chapter 1 Introduction 1
1.1 Background and Motivation 1
1.2 Main Contributions 5
1.3 Organization of the Dissertation 6
Chapter 2 Discrete-Time System with a Time-Varying State Delay 8
2.1 System Formulation 9
2.2 Stability Analysis of Nominal Systems with a Time- Varying State Delay 10
2.3 Output-Feedback Stabilization of Nominal Systems with Time-Varying State Delay 18
2.4 Stability Analysis of Uncertain Systems with a Time- Varying State Delay 21
2.5 Numerical Examples 23
2.6 Summary 28
Chapter 3 Discrete-Time System with a Time-Varying State Delay and Nonlinear Perturbations 29
3.1 System Formulation 30
3.2 Stability Analysis of Nominal Systems with a Time- Varying State Delay and Nonlinear Perturbations 31
3.3 Output-Feedback Stabilization of Nominal Systems with a Time-Varying State Delay and Nonlinear Perturbations 39
3.4 Numerical Examples 45
3.5 Summary 49
Chapter 4 Discrete-Time System with an Interval Time-Varying State Delay 50
4.1 System Formulation 51
4.2 Stability Analysis of Nominal Systems with Interval State Delay 52
4.3 Stability Analysis of Uncertain Systems with Interval State Delay 61
4.4 Numerical Examples 64
4.5 Summary 69
Chapter 5 Conclusions and Suggestions for Future Study 70
5.1 Conclusions 70
5.2 Suggestions for Future Study 72
Bibliography 74



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