以H-infinity平衡截斷法研究微分代數系統

Abstract

本文透過兩個퐻∞型態的「廣義代數黎卡提方程」將「H∞平衡截斷法」推廣至探討連續時間線性微分代數方程(描述子系統)的模型簡化問題，文中亦估算出了經H∞平衡截斷後的簡化系統與原系統以「間隙度量」為距離之精確誤差；而本文另一大重點為導出了「零D定理」，指出了在連續時間線性描述子系統中，任一給定的線性描述子系統(其D不為零)，皆可以等價為另一個(D為零)之線性描述子系統。

In this paper, by two H∞ generalized algebraic Riccati equations ,we generalize the method of H∞ balanced truncation to the problem of model reduction of linear time-invariant continuous-time differential-algebraic equations (descriptor systems) and we also derive the error of between the reduced system and the original system by using the so-called gap metric. On the other hand, we give and prove a new theorem, Zero-D theorem. According to this theorem, for any given linear time-invariant continuous-time descriptor system with D ≠ 0, it can be equivalent to another linear time-invariant continuous-time descriptor system with D = 0.