基于不变因子的传递函数矩阵的最小实现

journal6 ›› 2007, Vol. 28 ›› Issue (6): 13-17.

基于不变因子的传递函数矩阵的最小实现

（武汉工业学院数理科学系，湖北武汉 430023）

出版日期:2007-11-25 发布日期:2012-06-10
作者简介:高遵海（1966-），男，湖北钟祥人，武汉工业学院数理科学系副教授，博士生，主要从事控制理论与工程研究.
基金资助:
国家自然科学基金资助项目（79970025）；湖北省教育厅科学研究项目（D200618009）

Minimal Realization of Linear System Based on Invariant Factors of Transfer Function Matrix

(Department of Mathematics and Physics,Wuhan Polytechnic University,Wuhan 430023,China)

Online:2007-11-25 Published:2012-06-10

摘要/Abstract

摘要：基于传递函数矩阵的斯密斯-马克米兰（Smith-McMillan）标准型，讨论了以严真有理分式矩阵描述的传递函数矩阵的一个最小实现，其中每一个不变因子的最小实现对应一循环系统.如果斯密斯-马克米兰的秩为ｒ，那么最小实现对应于ｒ个循环系统的直和.特别地，当传递函数以行向量或列向量形式给出时和当系统矩阵以分块循环矩阵表示时，分别得到了能控或能观型实现，它们都是现有算法的改进.

关键词： 控制理论与控制工程, 定常线性系统, 传递函数矩阵, 不变因子, 最小实现

Abstract: Based on the Smith-McMillan normal form of a transfer function matrix，a kind of minimal realizations of a proper rational transfer function matrix are discussed.The minimal realization of each invariant corresponds to a cycle system.If the rank of the Smith-McMillan normal form of a transfer function matrix is ｒ,then the minimal realization corresponds to a direct sum of ｒ　cycle systems.Especially,the controllability canonical realizations and the observability canonical realizations are obtained when a transfer function matrix is the form of column vector or row vector and when the system matrix is the form of block circulant matrix,which are the improvement of current conclusions.

Key words: control theory and control engineer, time-invariant linear system, transfer function matrix, invariant factors, minimal realization

高遵海, 覃磊. 基于不变因子的传递函数矩阵的最小实现[J]. journal6, 2007, 28(6): 13-17.

GAO Zun-Hai, QIN Lei. Minimal Realization of Linear System Based on Invariant Factors of Transfer Function Matrix[J]. journal6, 2007, 28(6): 13-17.