Restricted complexity robust controllers for uncertain plants with rank one real perturbations

This paper addresses the problem of designing robust controllers for linear plants affected by rank one real perturbations. The main objective of the paper is to use a convex parameterization of robustly stabilizing controllers for optimizing the stability margin over an assigned class of restricted complexity controllers. In fact, it is well known that if no constraints on the controller structure are imposed, the complexity of the resulting optimal controller is usually excessive. This is the main objection commonly raised to practical applicability of robust design techniques. In this paper the problem of maximizing the real stability margin over an assigned class of controllers is considered. It is shown that such a problem can be made convex, provided the transfer function of a suitable filter is determined. Exploiting some properties of such a filter, an algorithm is devised for designing robust controllers. Such an algorithm, that requires the solution of a sequence of linear matrix inequalities feasibility problems, shows local convergence to the optimal controller in all the numerical examples worked out.