保结构及无源性的H_2模型降阶方法  

Structure-Preserving and Passivity-Preserving H_2 Model Order Reduction Method

作　　者：徐康丽[1] 杨志霞[1] 蒋耀林[1,2] 

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046 [2]西安交通大学数学与统计学院,陕西西安710049

出　　处：《计算机仿真》2015年第12期226-230,共5页Computer Simulation

基　　金：国家自然科学基金(No.11371287;No.11161045)

摘　　要：针对大规模线性系统的模型降阶问题,提出保结构与无源性的H2模型降阶方法。将原始系统传递函数进行泰勒展开得到传递函数的各阶矩,利用传递函数的各阶矩得到原始系统的传递函数与降阶系统的传递函数的H2范数表达式。根据原始系统所具有的特殊结构,运用多点二重Krylov子空间方法构造变换矩阵,从而得到原始系统在H2范数意义下的最佳降阶系统。所得到的降阶系统不仅能较好地模拟原始系统的动态行为,而且能保持原始系统的结构和无源性。数值算例验证了保结构与无源性的H2模型降阶方法是行之有效的。A structure -preserving and passivity- preserving H2 model order reduction method （SPHMOR） was presented for solving large - scale linear systems. The transfer function of the original system was expanded to obtain its moments and the HE norm error for the original system with its reduced - order system being derived by using their moments. Considering the special structure of the original system, the second - order Krylov subspaee method was used to construct the transformation matrix. Thereby, we can obtain a reduced - order system, which can be viewed as a well approximate system of the original system. The reduced - order system can obtain preserve the structure and the passivity of the original system. A simple numerical expreiment was conducted to illustrate the effectiveness of the proposed method.

关 键 词：模型降阶 降阶系统 无源性 矩匹配 

分 类 号：O29[理学—应用数学]