本論文探討具有廣義凸多邊形不確定量數位系統之數學模型的強韌穩定分析、強韌 H∞ 和 H2 性能的分析與設計。採用齊次多項式參數相依李亞普諾夫 (Homogeneous Polynomially Parameter Dependent Lyapunov, HPPDL) 矩陣的分析技巧，吾人將文獻中的結果推廣到更廣義的凸多邊形不確定系統之強韌穩定分析，並利用所推導出的線性矩陣不等式條件來設計狀態迴授控制器，使得閉迴路系統達到強韌 H∞ 和 H2 性能的要求。隨著齊次多項式矩陣階次的增加，則系統轉移矩陣的 H∞ 和 H2 範數值會接近其真實值的大小，同時以數值範例來驗證理論推導的結果。

This thesis addresses robust stability, robust H∞ and H2 performance and design of discrete-time polytopic systems with an LFT uncertainty assumed at each vertex. A sequence of relaxed sufficient analysis results based on the HPPDL matrix approach has been extended to cope with such more general uncertainty structure. The state feedback gain matrix to achieve robust H∞ and H2 performance can be easily computed from the derived sufficient LMIs. The larger the degree of homogeneous polynomial is, the lower H∞ and H2 norm are achieved. Numerical examples are included to illustrate the derived results.

摘要 i
符號表 iv
第一章 緒論 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 基本定義與結果 4
第三章 廣義凸多邊形不確定數位系統之 和 強韌性分析 9
3-1 節 廣義不確定數位系統的問題描述 9
3-2 節 系統之強韌穩定性分析 9
3-3 節 系統之強韌 和 強韌 的問題描述 14
3-4 節 系統之強韌 和 強韌 分析 15
3-5 節 數值模擬 19
第四章 廣義凸多邊形不確定數位系統之 和 控制器設計 23
4-1 節 系統之強韌 和 強韌 控制器設計的問題描述 23
4-2 節 系統之強韌 和 強韌 控制器設計 24
4-3 節 數值模擬 28
第五章 結論 31
參考文獻 32

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