基于F-M II状态空间模型的多维系统实现方法  

Multi-dimensional system realization method based on F-M II state space model

作　　者：陈君昊 程骅[1] 刘惠康[1] 盛道清[1] Chen Junhao;Cheng Hua;Liu Huikang;Sheng Daoqing(School of Information Science and Engineering,Wuhan University of Science and Technology,Wuhan 430080)

机构地区：[1]武汉科技大学信息科学与工程学院,武汉430080

出　　处：《高技术通讯》2021年第11期1202-1209,共8页Chinese High Technology Letters

基　　金：国家自然科学基金(61304129);国家重点研发计划(2017YFC0805100)资助项目。

摘　　要：针对多维系统的实现问题,本文对多输入多输出(MIMO)线性系统的FornasiniMarchesini II(F-M II)状态空间模型进行了研究。在一维系统实现方法的基础上做了进一步的讨论,提出了一种基于F-M II模型的多维系统实现矩阵的求解新方法。与规范的实现矩阵求解方法相比,新方法通过在传递函数特征多项式的图结构中添加两种类型的顶点,能够得到F-M II状态空间模型的一组完整的实现矩阵,而不是只有一个实现,且获得实现矩阵的阶次更低,避免了复杂的矩阵计算过程,使得系统表现形式更加清晰直观,有利于多维系统的设计和分析。对所提出的方法,本文给出了具体的数例说明其可行性。For the realization of multi-dimensional systems, the Fornasini-Marchesini II(F-M II) state space model of multiple-input multiple-output(MIMO) linear systems is studied. On the basis of the one-dimensional system realization method, a new multi-dimensional system realization matrix solution method based on F-M II model is proposed. Compared with the canonical form method, the proposed algorithm adds two types of vertices to the digraph of characteristic polynomials, a group of realization matrices of the F-M II state space model can be obtained instead of only one realization. And the order of the realization matrix is relatively low, avoiding the complicated matrix calculation process. The new method makes the system expression more clear and intuitive, and facilitates the design and analysis of multi-dimensional systems. For the proposed method, specific examples are given to illustrate its feasibility.

关 键 词：多维系统 多输入多输出(MIMO)系统 有向图 Fornasini-Marchesini II(F-M II)状态空间模型 实现矩阵 

分 类 号：O241.6[理学—计算数学]