本論文藉著線性矩陣不等式的方法來研究含有暫態響應的連續時間奇異系統可容許性與嚴格耗散性之分析及控制器的設計問題。
首先我們藉由在與效能指標滿足設計規格等價的線性矩陣不等式條件中，引入一個變數矩陣，將奇異系統的廣義 H∞ 控制結果，推廣到可適用任何奇異系統的模型。之後，為了設計狀態回授控制器我們推出對偶形式的等價條件。此結果不但能完成現有文獻在狀態回授控制器設計的存在必要條件證明，而且在數值計算上也比現有文獻簡單。
接下來我們將含有暫態響應的奇異系統之嚴格耗散控制，與廣義 H∞ 控制連結在一起，並設計狀態回授控制器與動態輸出回授控制器達到閉迴路奇異系統之可容和嚴格耗散。

In this thesis, we study the admissibility and the strict dissipativity analysis of the continuous-time singular systems with transients and its associated controllers design by means of linear matrix inequality (LMI) techniques.
Firstly, we extend the current generalized H∞ control result to singular systems without a norm-bounded constraint on its direct path gain matrices. Such a generalization is enabled by introducing an additional variable matrix in the linear matrix inequality conditions, whose feasibility is equivalent to performance index satisfying the design criterion. To facilitate the state feedback design, we then obtain the dual form of the LMIs. This result not only fulfils the necessity proof of the existing "sufficient only" state feedback design result, but it also simplifies the numerical simulation due to less variable being involved.
Finally, in terms of the linkage between strictly dissipative control and H∞ control, we extend the approach for generalized H∞ control to addressing the state feedback control and dynamic output feedback control design so that the closed-loop singular system is admissible and strictly dissipative.

目錄
摘要 ....................................................................................................................... i
表次 ...................................................................................................................... v
圖次 ..................................................................................................................... vi
符號表 ................................................................................................................ vii
第一章 緒論 ...........................................................................................................1
1-1 節 背景與動機 ................................................................................... 1
1-2 節 論文結構 ........................................................................................2
第二章 幾個矩陣性質.............................................................................................4
第三章 連續時間可容的奇異系統廣義 H∞ 範數分析與設計....................................6
3-1 節 系統描述 ....................................................................................... 6
3-2 節 奇異系統之可容許性與廣義 H∞範數定義........................................6
3-3 節 奇異系統之可容許與廣義 H∞ 範數分析.........................................10
3-4 節 奇異系統的廣義 H∞ 狀態回授控制器設計................................... 21
3-5 節 數值模擬 ..................................................................................... 29
第四章 含有暫態響應的可容許奇異系統之嚴格耗散性分析與控制器設計 .......... 31
4-1 節 含有暫態響應的可容許奇異系統之嚴格耗散性定義...................... 31
4-2 節 含有暫態響應的可容許奇異系統的之嚴格耗散性分析 ..................33
4-3 節 狀態回授控制器設計 ................................................................... 48
4-4 節 動態輸出回授控制器設計 ............................................................ 60
4-5 節 數值模擬 ..................................................................................... 82
第五章................................................................................................................ 95
結論 .................................................................................................................. 95
參考文獻 ........................................................................................................... 96

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