矩陣束之幾何結構及其在線性離散時間描述子系統之應用

Abstract

本論文探討矩陣束之重要幾何結構， 包括正規性、 特徵結構、 因果性等。 論文中亦探討回授允當化問題， 並研究線性離散時間描述子系統之Lyapunov理論。 文中並推導Lyapunov方程式對稱解及一般解存在之充分且必要條件， 並求出所有對稱解及一般解之表示式， 最後並舉兩個數值例子說明。

英文摘要 In this thesis we present geometric characterizations of fundamental properties of matrix pencils, such as regularity, eigenstructure and causality. We also deal with the feedback admissibilization problem and develop Lyapunov theory for linear discrete-time descriptor systems. Necessary and sufficient conditions are presented for the existence of a hermitian solution and general non-hermitian solution of Lyapunov equation. Explicit formulae, expressed in terms of the geometry of the underlying pencil, for all hermitian solutions and general non-hermitian solutions of the Lyapunov equation are also given. Finally, numerical examples are given for illustration.