In this paper, we present the sufficient and necessary condition for the sum of a identity matrix and a generalized cyclic matrix is nonsingular, and obtain the formal representation of the relative gain array of the sum matrix.

• 本文给出了单位矩阵与广义循环矩阵的和矩阵的非奇异的充要条件，得到了这样和矩阵的相对增益阵列的显示表达式。