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首先对ＭＩＭＯ或ＳＩＳＯ连续闭合线性系统在状态矩阵可交换下，给出了反馈阵存在的充要条件，即ＳＩＳＯ闭合系统归结到矩阵Ａ的特征值与特征根的情形，ＭＩＭＯ闭环系统归结到矩阵Ａ的特征子空间的不变性。而对于ＳＩＳＯ及ＭＩＭＯ开环系统情形时，以Ｋｒｏｎｅｃｋｅｒ积作为工具，将状态矩阵集可交换时反馈阵的存在性等价于Ｌｙａｐｕｎｏｖ方程解的存在性问题，同时给出了Ｌｙａｐｕｎｏｖ方程的具体形式。最后，通过几个具体数字例子来说明所得的结论。
Firstly, the necessary and sufficient conditions for the presence of feedback matrix are given under the interchangeability of state matrices for MIMO or SISO continuous closed linear systems, ie the SISO closed system is reduced to the eigenvalues and eigenvalues of matrix A. The MIMO closed-loop system is reduced to the matrix The invariant property of A’s subspace. In the case of SISO and MIMO open-loop systems, the existence of feedback matrix when the state matrix set is exchangeable is equivalent to the existence of solutions of the Lyapunov equation using the Kronecker product as a tool, and the concrete form of the Lyapunov equation is also given. Finally, the conclusions drawn from several specific numerical examples.