Solution building of Lyapunov equation for linear almost conservative systems

V.V.Novitskiy

Institute of Mathematics of Ukraine NAS, Kyev, Ukraine

Lyapunov matrix equation for linear stationary almost conservative systems has been investigated. An asymptotic expansion of a matrix-solution has been applied according to small parameter. A structure and a ceiling amount of free parameters have been found in the symmetric matrix, which is permutable with a skew-symmetric one, for effective construction of approximations. An algorithm for finding of a matrix-solution has been suggested in a case of various eigenvalues. The example is given.