Parametric H/sub /spl infin// loopshaping and weighted mixed sensitivity minimization

摘要

Generalized H/sub /spl infin// 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/sub /spl infin// 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/sub /spl infin// norm-bounded perturbations. Controller reduction is also investigated for the parametric H/sub /spl infin// loopshaping. Robust stability condition for using the reduced-order controller is established, and an estimate for the associated H/sub /spl infin// performance is obtained. Similar results are derived for normalized linear quadratic Gaussian (LQG) control.