Low-order robust controller design for interval plants

This paper deals with robust controller design for SISO linear plants subject to interval parametric uncertainty, a longstanding open problem of control theory. Based on Hermite-Fujiwara matrices and the generalized Kharitonov's theorem, a sufficient condition is derived for the existence of a robustly stabilizing controller of order up to three. This condition is formulated as a non-convex rank-one LMI feasibility problem in the controller parameters. This optimization problem is addressed by two standard heuristics relying upon semidefinite programming. In spite of the potentially conservative nature of the stabilizability condition and the lack of convergence of the proposed algorithms, several numerical examples bear out the usefulness of our approach for designing robust controllers of small order at low computational cost.