理學院: 數學研究所指導教授: 容志輝; 張志中許惟喬Hsu, Wei-ChiaoWei-ChiaoHsu2017-03-062018-06-282017-03-062018-06-282015http://ntur.lib.ntu.edu.tw//handle/246246/276749本文透過兩個⻒7;∞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 = 0.1306418 bytesapplication/pdf論文公開時間: 2017/2/16論文使用權限: 同意有償授權(權利金給回饋學校)廣義代數黎卡提方程平衡截斷微分代數方程描述子系統模型簡化間隙度量零D定理generalized algebraic Riccati equationsbalanced truncationdifferential-algebraic equationdescriptor systemsgap metricZero-D Theoremthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/276749/1/ntu-104-R01221017-1.pdf