On the synthesis of restricted complexity controllers for uncertain plants with ellipsoidal perturbations

The problem of restricted complexity stability margin maximization (RCSMM) for SISO plants affected by rank one real perturbations is considered. This problem amounts to maximizing the l₂ parametric stability margin over an assigned class of restricted complexity controllers, described by rational transfer functions of fixed order with coefficients depending affinely on some free parameters. It is shown that the RCSMM problem, which in general admits local maxima, can be approached by means of convex optimization techniques. Specifically, an optimization procedure, which requires at each step the computation of a rational function via polynomial factorization and the solution of an LMI feasibility problem with respect to the free controller parameters, is devised