Direct Synthesis of Fixed-Order ${\cal H}_{\infty}$ Controllers

This technical note considers the fixed-order H
_∞
output feedback control design problem for linear time invariant (LTI) systems. The objective is to design a fixed-order controller with guaranteed stability and closed-loop H
_∞
performance. This problem is NP-hard due to the non-convex rank constraint which appears in the formulation. We propose an algorithm for noniterative direct synthesis (NODS) of reduced order robust controllers. NODS entails initial computation of two positive-definite matrices via full-order convex LMI conditions. These are then utilized by appropriate eigenvalue decomposition to directly obtain a suboptimal convex formulation for the fixed-order controller.