状态反馈极点配置的直接方法

本文研究了线性时不变系统x=Ax+Bu,y=Cx,引进状态反馈u=-Kx任意配置闭路极点问题.文中通过矩阵[sI-A]-1B的右既约分解矩阵,导出了闭路系统特征方程的p×p维多项式矩阵行列式表示式(p=rankB).利用这一表示式直接配置闭路极点,计算反馈矩阵K.文中同时给出了计算矩阵[sI-A]-1B右既约分解矩阵的一种新算法.最后举例说明了它们的应用,并进一步讨论了K矩阵的灵活算法.

A Direct Method for Pole Assignment Using State Feedback

In this paper the problem of the pole assignment in a linear time-invariant systemx=Ax+Bu, y=Cx, using the state feedback law u=Kx is studied. In the paper adeterminant experession of the p×p polynomial matrix for the characteristic polynomialof the closed-loop system is derived by means of the relative right reduced factorizationmatrices of the matrix [sI-A]-1B(p=rakB). Based on the expression thepoles are assigned directly and the matrix K is computed. In addition a new algorithmfor computing the relative right reduced factorization matrices of the matrix [sI-A]-1Bis presented. Finally, a numerical example is given to illustrate their applications, andby means of the example flexible computation of the matrix K is further shown.