## ON SOLUTION OF MODIFIED MATRIX SYLVESTER EQUATION

## *F. A. Aliev, V. B. Larin*

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## Abstract

In the paper, the approach connected with the linear matrix inequalities for construction of solution of the modied Sylvester matrix equations, is used. The essence of the approach consists in replacement the initial equation with complex matrices, by two equations with real matrices. That allows to use for their solution the procedures of linear matrix inequalities. Eciency of oered algorithm is shown on the examples.

## Keywords

linear matrix inequalities (LMI), matrix Sylvester equation, modied Sylvester equation, complex matrices