Let the system
be stabilized by the
th order controller
. According to El Ghaudi and Gabinet, the existence of the stabilizing controller can be reduced to a MIN-RANK problem: find min rank
, subject to
symmetry preserving on the space of symmetric matrices,
symmetric and the ordering is to be interpreted in the sense of Löwner:
is positive definite. The authors’ method of solving the problem employs idea from the ordered linear complementarity theory and the notion of the least element in a vector lattice.