A convex parametrization of suboptimal hinfini controllers
Résumé
A new parametrization is proposed for suboptimal H controllers of order no larger than the plant order. Here such controllers are generated from pairs of symmetric matrices (X,Y) constrained by two Riccati matrix inequalities and some positivy requirements. Interestingly, the Riccati expressions and the positivity conditions are exactly those arising in the usual state-space solution of suboptimal H problems. When working with the inverses R and S of X and Y, respectively, the constraints can be rewritten as linear matrix inequalities which define a convex parameter set. This sets up a convenient framework to handle design objectives which can be reflected in terms of (R,S). Examples of such objectives include reduced-order H design and the avoidance of pole/zero cancellation between the plant and the controller.