SENSITIVITY LIMITATIONS IN NONLINEAR FEEDBACK-CONTROL

In this paper we define nonlinear sensitivity and complementary sensit ivity operators of a feedback control loop and show that they satisfy a complementarity constraint. We then consider the case of general non linear open-loop operators that give rise to nonlinear sensitivities t hat are Lipschitz operators on some Banach space. Under these conditio ns, we obtain lower bounds on the Lipschitz constants of both operator s for open-loop nonminimum phase and unstable nonlinear systems. These results parallel those known in linear control theory on the H-infini ty norms of S and T. We finally point to the relevance of the defined nonlinear sensitivities in robustness issues.