Biaffine matrix inequality properties and computational methods

Many robust control synthesis problems, including μ/k_m-synthesis, have been shown to be reducible to the problem of finding a feasible point under a biaffine matrix inequality (BMI) constraint. The paper discusses the related problem of minimizing the maximum eigenvalue of a biaffine combination of symmetric matrices, a biconvex, nonsmooth optimization problem. Various properties of the problem are examined and several local optimization approaches are presented, although the problem requires a global optimization approach in general.