本論文擬以線性矩陣不等式為工具來探討描述系統之根叢集判定問題；我們推導出一充分且必要的線性矩陣不等式條件來同時判別一個描述系統的正規性、脈衝免疫性及有限特徵值落於廣義線性矩陣不等式區域內。由於一般控制系統皆具有不確定量的存在，因此，我們對二種不確定量，即範數有界和凸多邊形不確定量，分別提出充分條件來保證不確定描述系統的強健根叢集特性。最後，我們提出以線性矩陣不等式為基礎的狀態迴授控制器設計法則，並提出數個範例之模擬結果以說明前述理論之正確性和可行性。

In this thesis, an LMI-based pole-clustering characterization for descriptor systems is investigated. A necessary and sufficient condition for checking simultaneously the regularity, impulse immunity, and finite eigenvalues locating in the generalized LMI regions is derived. Since uncertainty exists inevitably in control systems, we propose two sufficient conditions to guarantee the robust pole clustering in the generalized LMI regions for uncertain descriptor systems with two types of uncertainties, i.e. the norm bounded uncertainty and the convex polytopic uncertainty. The LMI-based state feedback controller design methods are developed as well. Finally, the validity and the feasibility of our theoretical results are verified by the numerical simulation results of several examples.

摘要 i
符號表 iv
第一章 序論 1
　　1-1 節　文獻回顧與研究動機 1
　　1-2 節　論文綱要 3
第二章 描述系統之根叢集分析 4
　　2-1 節　系統基本性質與數學基礎 4
　　2-2 節　廣義線性矩陣不等式區域－ 區域 6
　　2-3 節　根叢集於 區域之分析 9
第三章 描述系統之強健根叢集分析 16
　　3-1 節　問題描述 16
　　3-2 節　具範數有界不確定量之強健根叢集於 區域之分析 18
　　3-3 節　具凸多邊形不確定量之強健根叢集於 區域之分析 24
第四章 控制器設計與數值模擬 29
　　4-1 節　狀態迴授控制器設計 29
　　4-2 節　數值模擬 33
第五章 結論 47
參考文獻 48

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