Explicit direct solution of the Lyapunov matrix equation
In the proposed method of explicit direct solution for the Lyapunov matrix equation, the author starts from the decomposition of a square matrix formed as a product of the constant coefficient matrix of a linear dynamic system and the searched Lyapunov matrix into a sum of symmetric and skew-symmetric matrices. The Lyapunov matrix equation is just the symmetric part of the decomposed matrix. To this equation is added another one representing the skew-symmetric part, and the obtained equation provides direct and explicit solution for the algebraic Lyapunov equation. In comparison with other direct solutions, the proposed method requires in addition the inverse of the constant coefficient matrix, but the set of linear algebraic equations to be solved is reduced by the order of magnitude equal to the dimension of the considered system. Some examples are given to illustrate the computational effort of the proposed method.
scientific article; zbMATH DE number 4159977
scientific article