本論文主要是以可轉換連續型與散型控制系統的凱利變換為基礎，運用並根據保結構法(SDA)的概念，發展一套G-SDA法，來求解廣義連續型及離散型的黎卡迪方程。文中依各類型，分別列舉在矩陣E條件數偌大的情況下，本法的數值結果，以說明G-SDA法的有效性與特色。

In this paper we extend the structure-preserving doubling algorithm (SDA) to compute the symmetric positive semi-definite solutions of the generalized continuous as well as discrete algebraic Riccati equations. Our main idea is to relate continuous and discrete time control systems based on the generalized Caley transformation.
In the end, we select some examples to illustrate that the G-SDA performs better than the MATLAB commands in the control toolbox.

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