Low-order robust controller design for interval plants

This paper deals with robust controller design for SISO linear plants subje ct to interval parametric uncertainty, a longstanding open problem of contr ol theory. Based on Hermite-Fujiwara matrices and the generalized Kharitono v's theorem, a sufficient condition is derived for the existence of a robus tly stabilizing controller of order up to three. This condition is formulat ed as a non-convex rank-one LMI feasibility problem in the controller param eters. This optimization problem is addressed by two standard heuristics re lying upon semidefinite programming. In spite of the potentially conservati ve nature of the stabilizability condition and the lack of convergence of t he proposed algorithms, several numerical examples bear out the usefulness of our approach for designing robust controllers of small order at low comp utational cost.