Lyapunov引理的一个构造性证明及其应用

A constructive proof of Lyapunov lemma and its applications

给出Lyapunov引理的一个构造性证明,利用它证明了矩阵方程AX+XA=B的解的存在性和唯一性,并且找到它的唯一解。给出Lyapunov引理在锥优化问题中的应用。

In this paper,we give a constructive proof of Lyapunov lemma.We prove the existence and uniqueness of the solution of the matrix equation AX＋XA = B by using Lyapunov lemma.Finally,we present application of Lyapunov lemma in conic programming.