本論文考慮具區間時變延遲的離散時間系統的穩定性分析與H∞性能分析，並且推廣至具範數有界不確定量系統的強韌穩定性分析、強韌H∞性能分析和強韌H∞狀態回授控制器設計。藉由定義新的Lyapunov functional和結合延遲分段的方法來改善現有文獻所提出的結果，得到了較不保守的線性矩陣不等式的條件來保證系統的漸近穩定。每一章都有數值模擬來說明我們所提出的方法的好處。

This thesis concerns stability analysis and robust H∞ performance analysis for discrete-time systems with interval time-varying delay; moreover, the results are extended to the systems with norm-bounded uncertainties. By defining a novel Lyapunov functional and combining delay partition methods to improve the results in existing literature, we obtain a less conservative linear matrix inequality condition to guarantee the asymptotic stability for the discrete-time systems. There are examples to illustrate the advantage of our method in every chapter.

摘要 i
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 2
第二章 矩陣性質與數學基礎 3
第三章 離散延遲系統之 H∞ 性能分析 5
3-1 節 離散延遲系統之穩定性分析 5
3-2 節 離散延遲系統之 H∞ 性能分析 21
3-3 節 數值模擬 27
第四章 離散系統之延遲相關強韌 H∞ 分析 30
4-1 節 問題描述 30
4-2 節 離散延遲系統之強韌穩定性分析 31
4-3 節 離散延遲系統之強韌 H∞ 分析 35
4-4 節 數值模擬 38
第五章 離散系統之延遲相關強韌 H∞ 設計 43
5-1 節　離散延遲系統之強韌 H∞ 設計 43
5-2 節　數值模擬 50
第六章 結論 52
參考文獻 53

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