Eigenvalue lower bounds for solutions to systems of matrix equations

Abstract

The systems of matrix equations
AXBT + BXTAT = C;
DXET + EXTDT = F; (I)
AXBT + BXAT = C;
DXET + EXDT = F; (II)
( including various matrix equations as a special case ) have nice applications in various branches of control
and system theory. In this paper, the inequalities which are satised by the determinant of the solutions
to the systems of matrix equations (I) and (II) are proposed. By applying these inequalities, lower bounds
for the product of the eigenvalues of the solutions to the systems of matrix equations (I) and (II) are
established.