A matrix sign function based solution of parameter dependent Sylvester equations

This paper focuses on some parameter dependent Sylvester equations arising in systems and control theory. The matrices involved are assumed to be i) parameter dependent, ii) not necessarily of the same size, and iii) with possible common eigenvalues depending on the parameter value. A matrix sign function based solution is proposed, considering two main cases: the square coefficient matrices are diagonalizable or block-diagonalizable.