Parametric H-x loopshaping and weighted mixed sensitivity minimization

Generalized H-infinity loopshaping is developed for a particular weighted m ixed sensitivity minimization task, A Free parameter is introduced to trade off minimizations of sensitivity and complementary sensitivity in the H-inf inity performance index. A quadratically convergent algorithm is derived fu r computing the optimal performance index, and a state-space solution is ob tained for suboptimal controllers. These results are applicable to stabiliz ation of uncertain systems where normalized coprime Factors involve paramet rically weighted H-infinity norm-bounded perturbations. Controller reductio n is also investigated for the parametric H-infinity loopshaping. Robust st ability condition for using the reduced-order controller is established, an d an estimate for the associated H-infinity, performance is obtained. Simil ar results are derived for normalized linear quadratic Gaussian (LQG) contr ol.