On the solution of the matrix Sylvester equation
Journal Title: Дослідження в математиці і механіці - Year 2014, Vol 19, Issue 1
Abstract
Lyapunov matrix equations and their generalizations — Sylvester matrix equation widely used in the theory of stability of motion, as well as the solution of differential Riccati and Bernoulli equations. If the structure of the general solution of the homogeneous part of the Lyapunov equation is well studied, the solution of the inhomogeneous equation Sylvester and, in particular, the Lyapunov equation is quite cumbersome. The article suggests the solvability conditions, as well as a scheme for constructing a particular solution of the inhomogeneous equation based on Lyapunov type pseudo-operator corresponding to the homogeneous part of the Lyapunov equation. The paper proposes a structural formula for constructing a particular solution of the inhomogeneous equation Sylvester and, in particular, the Lyapunov equation.
Authors and Affiliations
S. M. Chuiko
Keywords
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