误差检验式是线性系统误差检验中常用的关系式。本文首先建立了误差检验式的时域和频域之间的关系。由此出发,证明了只要得到多项式矩阵[C’(zI-A)’]’的左零空间的基,则可得到所有的误差检验式;证明了用“按行搜寻格子”(Searching the Crate by Rows)的方法可以得到[C’(zI-A)’]’的左零空间的最小基,从而得到误差检验式的频域方法。 Error test is a linear system error test commonly used in the relationship. In this paper, the relationship between time-domain and frequency-domain of error-checking is first established. Starting from this, we prove that we can get all the error test formulas as long as we get the base of the left null space of the polynomial matrix [C ’(zI-A)’] ’; we prove that using the "Searching the Crate by Rows), the smallest base of the left zero space of [C ’(zI-A)’] ’can be obtained and the error-checking frequency domain method is obtained.