MIMO系统转化为Luenberger能控规范型的条件

江宁强; 宋文忠

引用本文:	江宁强, 宋文忠.MIMO系统转化为Luenberger能控规范型的条件[J].控制理论与应用,2007,24(5):866~868.[点击复制]
	JIANG Ning-qiang, SONG Wen-zhong.Restraint on MIMO system in being transformed into the Luenberger’s canonical form[J].Control Theory and Technology,2007,24(5):866~868.[点击复制]

MIMO系统转化为Luenberger能控规范型的条件

Restraint on MIMO system in being transformed into the Luenberger’s canonical form

摘要点击 2432 全文点击 1657 投稿时间：2005-12-22 修订日期：2007-04-11

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DOI编号 10.7641/j.issn.1000-8152.2007.5.034

2007,24(5):866-868

中文关键词线性系统能控规范型极点配置能控性指数

英文关键词 linear system controllable canonical form pole assignment controllability index

基金项目

作者	单位
江宁强, 宋文忠	南京理工大学自动化学院, 江苏南京210014 东南大学自动化研究所, 江苏南京210096

中文摘要

线性系统化为Luenberger能控规范型后可以很方便地进行极点配置. 本文证明, 在完全能控的情况下,MIMO系统能否化为Luenberger能控规范型与系统的最大能控性指数和最小能控性指数之差有关. 如果两者之差大于1, 就可能在控制矩阵B中除第l行(l=\sum\limits_{i=1}^{m} \mu_i, 1<=m<=r )以外的位置上出现非零元. 结果表明, 用Luenberger能控规范型方法进行极点配置有一定的局限性.

英文摘要

Pole assignment can be readily implemented after the linear system is transformed into the Luenberger’s canonical form. It is proved that the difference between the maximal and the minimal controllability indices is the essential condition to ensure that whether a controllable MIMO system can be transformed into the Luenberger’s canonical form or not. If the difference is greater than 1, non-zero elements may then appear in the control matrix B except at the row l(l=\sum\limits_{i=1}^{m} \mu_i, 1<=m<=r ). The result also shows the restraint of this method in pole assignment.