Parametric H∞ loopshaping and weighted mixed sensitivity minimization

Generalized H 1 loopshaping is developed for a particular weighted mixed sensitivity minimization task. A free parameter is introduced to trade-oo minimizations of sensitivity and complementary sensitivity in the H 1 performance index. A quadratically convergent algorithm is derived for computing the optimal performance index and a state-space solution is obtained for suboptimal controllers. These results are applicable to stabilization of uncertain systems where normalized coprime factors involve parametrically weighted H 1 norm bounded perturbations. Controller reduction is also investigated for the parametric H 1 loopshaping. Robust stability condition for using the reduced order controller is established and an estimate for the associated H 1 performance is obtained. Similar results are derived for normalized LQG control.