Explicit solution of lyapunov equation using arrow form matrix

摘要

The aim of this paper is to determine an explicit solution of the Lyapunov equation by using the arrow form matrix. The main result points out that, if the unknown matrix is (n x n), the solution can be determined through the inversion of only a ((n-1)x(n-1)) explicit matrix. An illustrative example shows the simplicity of the use of the proposed method and the easiness of the physically interpretation of results.