A new feedback optimization problem

Summary form only given. Methods for stabilizing a plant P with an affordable variable structure ΔP are derived, starting with an operator optimization problem. When C represents the series compensator, ΔC the series compensator which is activated when ΔP is present, F the feedback compensator, ΔF the feedback compensator which is activated when ΔP is present, r the reference input, and d_i, i=1, 2, 3 the additive disturbances, the objective is to ensure that the closed-loop transmissions satisfy performance objectives for stabilizing ΔP, C, C+ΔC, and F +ΔF. Another way of considering the problem is to aim at the minimization of the norm of the difference between the output of the undisturbed nominal system and the output of the modified system with disturbances. It is possible to reconsider the designs while assuming that ΔP is a nonlinear flexible structure. Modelling uncertainties δP could then be taken into consideration in order to develop robustness bounds for each of the previous designs