矩阵数值秩的一种确定方法及其在控制系统中的应用

一、矩阵的数值秩 矩阵秩的确定在现代控制理论中占有重要的地位。在代数理论中,用行列式或特征值来判断矩阵的秩,由于舍入误差的存在,用计算机判断矩阵秩时,这些方法是不完全适用的。

DETERMINATION OF THE NUMERICAL RANK OF A MATRIX AND IT'S APPLICATION TO CONTROL SYSTEM ANALYSIS

The determination of the numerical rank of a matrix by using computer and its application to control system analysis is discussed. It is shown by some typical examples that the traditional concept of rank and algorithm for its determination are not suitable for numerical computation. The concept of numerical rank and algorithm for its determination are then introduced. The singular value decomposition is employed in this algorithm. The numerical stability of the algorithm is analysed. Furthermore, the algorithm is applied to the determination of controllability and observability of control systems. As an example, the alignment of a Schuler platform is discussed.