A convex parametrization of H/sub infinity / suboptimal controllers

A novel parametrization is proposed for the set of H/sub infinity / 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 rho (XY)<or= gamma /sup 2/. The formalism is identical to that involved in the characterization of suboptimal gamma '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/sub infinity / 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 gamma -suboptimal controllers. Applications to reduced-order H/sub infinity / design are also discussed.<<ETX>>