Parametric H∞ loopshaping and weighted mixed sensitivity minimization

Generalized H_∞ loopshaping is developed for a particular weighted mixed sensitivity minimization task. A free parameter is introduced to tradeoff minimizations of sensitivity and complementary sensitivity in the H_∞ 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_∞ norm-bounded perturbations. Controller reduction is also investigated for the parametric H_∞ loopshaping. Robust stability condition for using the reduced-order controller is established, and an estimate for the associated H_∞ performance is obtained. Similar results are derived for normalized linear quadratic Gaussian (LQG) control