Optimal weighted performance of the generalized linear control system with uncertainty

The optimal performance under the effect of the plant uncertainty is investigated in this paper. The plants with the relative degree zero and one considered are unstable. The uncertain disturbance problem is formulated by utilizing stochastic embedding of the uncertainty. The expectation of the H₂ norm for the weighted tracking sensitivity error between the nominal system and the true system is defined and minimized by adjusting the true controller. The optimal redesign controller are derived. One example is given to evaluate the optimal weighted performance. It is shown that it is hard to control the system as the unmodeled gain increases.