Parameterized Solution to a Class of Sylvester Matrix Equations

A class of formulas for converting linear matrix mappings into conventional linear mappings are presented.Using them,an easily computable numerical method for complete parameterized solutions of the Sylvester matrix equation AX-EXF=BY and its dual equation XA-FXE=YC are provided.It is also shown that the results obtained can be used easily for observer design.The method proposed in this paper is universally applicable to linear matrix equations.