臺灣博碩士論文加值系統

在這篇論文中，我們主要研究描述子系統之廣義連續時間代數 Riccati 方程式。最主要定理是證明由 Hamiltonian 矩陣對所推導出的非對稱廣義連續時間代數 Riccati 方程式，其存在穩定解的充分且必要的條件。其次，推廣已知的連續時間代數 Riccati 方程式的性質到非對稱廣義連續時間代數 Riccati 方程式之論證。

In this thesis, the generalized continuous-time algebraic Riccati equation (GCARE) for descriptor systems is studied.
The necessary and sufficient condition for the existence of
stabilizing solutions to a nonsymmetric generalized algebraic Riccati equations is derived based on a Hamiltonian matrix pencil approach. Some of the generalizations of the well known properties of the algebraic Riccati equation to the GCARE case are also proposed.

1. Introduction 1
2. Preliminaries 4
2.1 Notations and Definitions ............................ 4
2.2 Elements of Descriptor Systems Theory ............... 8
2.3 Generalized Continuous-time Algebraic Riccati Equations 15
3. Main Results 18
4. Conclusions 38

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