• 作者： 黃奇; 容志輝
• 作者服務機構： 國立成功大學化學工程學系; 電機工程學系
• 中文摘要： 本文提出一種新的運算法則，從間斷時問系統的時問慣量和馬可夫參數計算Z轉移函數對Z=1與Z＝∞交替展開之Cauer連分式。根據此連分式，我們建立了系統狀態實現方塊圖，並衍導出其相對應之狀態空間模式。由此一型式的狀態空間方程式，我們可直接利用矩陣分割法求得降因次簡化模式。此外，文中亦提出了連分式之狀態空問模式與相位變數的狀態空間模式之相似變換矩陣，以建立關聯原系統模式和簡化模式之狀態的近似群聚矩陣。
• 英文摘要： A new algorithm is presented for obtaining the Cauer continued-fraction expansion (CFE) about z＝1and z=∞ alternately, of the z-transfer function of a linear time-invariant discrete-time system from itstime-moments and Markov parameters. A realization of the continued-fraction expansion and the cor-responding CFE canonical state-space model are developed. Thus, reduced state-space models of variousorders can be readily obtained by directly partitioning the respective matrices of this CFE canonical state-space model. The relationships between the states of the original system, and the state vectors of its re-duced-order CFE models are also established through constructing a similarity trans-formation matrixwhich transforms a general original state-space model to the CFE canonical state-space model.
• 中文關鍵字： linear systems; discrete systems; approximation; continued fractions
• 英文關鍵字： --