LMI optimization for fixed-order H∞ controller design

A general H_∞ controller design technique is proposed for scalar linear systems, based on properties of positive polynomial matrices. The order of the controller is fixed from the outset, independently of the order of the plant and weighting functions. A sufficient LMI condition is used to overcome non-convexity of the original design problem. The key design step, as well as the whole degrees of freedom are in the choice of a central polynomial, or desired closed-loop characteristic polynomial.