Reliable computation of H∞ central controllers near the optimum

Abstract

The state-space formulas for the usual H_∞ central controller become singular when approaching the optimum γ_opt. A new approach is taken to circumvent this difficulty. It consists of extending the notion of central controller to include proper controllers with a feedthrough term. While such controllers are still derived from the usual Riccati solutions X_∞, and Y_∞, their feedthrough gain can be selected so as to neutralize the singularities near γ_opt. This provides numerically stable formulas for the controller parameters and eliminates the discontinuity between the realizations of nearly optimal and of reduced-order optimal central controllers. The advantages of this method are illustrated on a few examples.