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

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 from i=1 to m μi,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.

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=^m∑i=1 μi,1≤m≤r）.The result also shows the restraint of this method in pole assignment.