自由离散系统的状态方程为:X(K+1)=AX(K),初值为X(0)(1)其中A为n×n阶常矩阵,X(0)为n阶矢量利用递推公式立即得到:X(K)=A~KX(0)(2)上式中含A~K,对于X(K)变化的性质不够明确。现利用特征值的方法,在参考书目1中讨论了A阵的特征值互不相等的情况。本文讨论有相同特征值的情况。1.A阵的特征值互不相等时:设特征方程为|A-λ1|=0=(λ-λ_1)(λ-λ_2)…(λ-λ_n), The state equation of free discrete system is: X (K + 1) = AX (K), initial value is X (0) (1) where A is n × n order normal matrix, Push the formula immediately: X (K) = A ~ KX (0) (2) A ~ K in the above formula, the nature of the change of X (K) is not clear enough. Now use the eigenvalues ​​approach, in the bibliography 1 discusses the A array of eigenvalues ​​are not equal to each other. This article discusses the case of the same eigenvalue. 1.A array of eigenvalues ​​are not equal to each other: Let the characteristic equation is | A-λ1 | = 0 = (λ-λ_1) (λ-λ_2) ... (λ-λ_n)