On the solving of matrix equation of Sylvester type

Document Type : Research Paper


1 Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan

2 Institute of Mechanics of the Academy of Sciences of Ukraine, Ukraine, Kiev


A solution of two problems related to the matrix equation of Sylvester type is given. In the first problem, the procedures for linear matrix inequalities are used to construct the solution of this equation. In the second problem, when a matrix is given which is not a solution of this equation, it is required to find such solution of the original equation, which most accurately approximates the given matrix. For this, an algorithm for constructing a general solution of the Sylvester matrix equation is used. The effectiveness of the proposed approaches is illustrated on the examples.