本篇論文應用廣義界實引理(Bounded real lemma)及一些線性代數方程式的結果,來推導出離散時間描述子系統之H∞靜態輸出回授控制有解的充分且必要條件為存在一個對稱且可逆矩陣(invertible symmetric)滿足某些廣義離散時間代數Riccati不等式(generalized discrete-time algebraic riccati inequality),並求出靜態輸出回授控制器的所有解.

In this dissertation ,based on Bounded Real Lemma and some recent results of linear algebra equation we derive a necessary and sufficient condition for the solvability of
H∞ control problem for discrete-time descriptor systems using static output feedback in terms of the existence of a invertible symmetric matrix satisfying a certain generalized
discrete-time algebraic Riccati inequality (GDARI).
A parametrization of all static output feedback controllers is also provided.

1 簡介
2 數學基礎與背景知識
2.1 離散時間描述子系統之數學描述
2.2 離散時間描述子系統H∞問題敘述
2.3 廣義界實引理(Generalized Bounded Real Lemma)
2.4 Pseudo-inverse與線性方程式
3 H∞靜態輸出回授控制
3.1 H∞狀態回授控制器設計
3.2 H∞靜態輸出回授控制器設計
4 結論與未來展望

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