LMIRank

The linear matrix inequality (LMI) problem is a well known type of convex feasibility problem that has found many applications to controller analysis and design. The rank constrained LMI problem is a natural as well as important generalization of this problem. It is a nonconvex feasibility problem de¯ned by LMI constraints together with an additional matrix rank constraint. Interest in rank constrained LMIs arises as many important output feedback and robust control problems, that cannot always be addressed in the standard LMI framework, can be formulated as special cases of this problem [10], [37], [16], [30]. Examples include bilinear matrix inequality (BMI) problems, see [16] and [30], that are easily seen to be equivalent to rank one constrained LMI problems.