Low-order H∞ synthesis via LMIs

The existence of low-order H_∞ controllers can be fully characterized by a system of linear matrix inequalities (LMI) together with a rank constraint. Due to this rank constraint, the corresponding optimization problem is nonconvex and much harder than pure LMIs. Nevertheless, it can be attacked by a number of optimization techniques. One possible approach is discussed in this paper. Here adequate solutions are sought by solving a smooth constrained optimization problem. Numerical experiments show that this scheme often succeeds in significantly reducing the controller order.