A convex parametrization of H∞ suboptimal controllers

A novel parametrization is proposed for the set of H_∞ suboptimal controllers of order no larger than the plant order. Unlike the classical Q-parametrization, this representation is state-space-oriented, and the controllers are generated from solutions of two algebraic Riccati inequalities (ARIs) coupled by the constraints X>0, Y>0, and ρ( XY)⩽γ². The formalism is identical to that involved in the characterization of suboptimal γ´s, except that strict inequalities replace equalities. In addition, the parameter set defined by these ARIs is convex. This parametrization opens new perspectives for H_∞ design. Some interesting problems can indeed be formulated as convex optimization problems in this framework, e.g., the maximization of internal stability margins over all γ-suboptimal controllers. Applications to reduced-order H_∞ design are also discussed