广义系统反馈稳定性问题的一种算法

Algorithm for Feedback Stability of Singular System

针对广义系统的反馈稳定性问题,该文应用亚负定矩阵、矩阵的广义左逆等给出了广义系统反馈稳定性问题的一种算法。引入状态反馈律得到广义系统的闭环系统;求出该闭环系统的解;令闭环系统的解的指数部分的矩阵等于某一亚负定矩阵,即可求出使广义系统稳定的反馈矩阵。最后给出算例说明所给方法的应用。

Aiming at the problem of the feedback stability of a singular system,this paper gives an algorithm to solve this problem by using sub-negative definite matrix and generalized left inverse of matrix.The closed loop system of singular system is obtained by introducing the state feedback law;the solution of the closed loop system is obtained;the matrix in exponent of the solution of the closed loop system is let equal to a sub-negative definite matrix,then the feedback matrix which makes the singular system stable can be obtained.An example is given for the application of the method.