本論文探討線性不確定連續延遲系統的延遲相關、強韌穩定性分析、和狀態回授控制器設計問題。藉由新選定的Lyapunov-Krasovskii泛函，結合現有文獻中一些可減少條件保守性的方法，推得會確保系統漸近穩定的線性矩陣不等式充分條件，並進而証明新的穩定條件確實比現有文獻中的一些結果更好。另外，並用新推得的條件為基礎，來做狀態迴授控制器設計。在論文主要內容的三章裡，都有附上電腦模擬的數值結果，藉以驗證理論推導的結果。

This thesis concerns delay-dependent robust stability analysis and stabilization for time-delay system with uncertainties. By choosing new Lyapunov-Krasovskii functional and using methods which can reduce conservativeness of stability condition in the literature, new delay-dependent sufficient stability conditions are obtained in terms of linear matrix inequality. It is shown that the new stability conditions can provide less conservative results than some existing ones. Furthermore, the new stability conditions are also used to design the state feedback controllers. Finally, numerical examples are given to show the derived results and compared with results in the literature.

目 錄
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 2
第二章 延遲系統之延遲相關穩定性分析 3
2-1節 問題描述與數學基礎 3
2-2節 延遲系統穩定性分析 4
2-2-1節 自由權重矩陣法 4
2-2-2節 詹生不等式法 18
2-2-3節 延遲分解法 25
2-2-4節 凸組合於延遲法 32
2-3節 數值模擬 38
第三章 延遲系統之延遲相關強韌穩定性分析 42
3-1節 問題描述 42
3-2節 具範數有界不確定量之強韌穩定性分析 43
3-3節 具凸多邊型不確定量之強韌穩定性分析 46
3-4節 數值模擬 54
第四章 控制器設計 62
4-1節 狀態迴授控制器設計 62
4-2節 數值模擬 66
第五章 結論 72
參考文獻 73

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