Reliable computation of H infini central controllers near the optimum

Projet META2The state-space formulas for the usual H central controller become singular when approaching the optimum gopt. 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 gopt. 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