不改变系统能观性的状态反馈的存在性

Existence of a State Feedback of not Changing the Observability of the System

现代控制论对能控、能观但不稳定的系统,可用一个线性状态反馈使其变得稳定,并保持系统的能控性不变,但对于这种反馈是否也能保持系统的能观性不变则没有讨论,这是一个理论上的缺憾。这里就一类定常离散系统对这个问题进行了研究,由矩阵的特征根及矩阵的秩与线性定常离散系统的稳定性及能观性的关系,用构造的方法证明了不改变系统能观性的状态反馈的存在性,并给出了构造这种反馈的方法。

By modern cybernetics, we can find out a state feedback for a linear time system, which does not change the controllability and stability of the system. But whether a state feedback for linear time system can be found out, which does ont change observability of the system or not, so far hasn't been discussed. The problem is studied according to the steady discrete time linear system, and a state feedback is found out, which does ont change the controllability, observability and stability, by relation of stability, observability and characteristic root, rank of matrix, of steady discrete time linear system; the method of how to construct the state feedback is given.