Sensitivity limitations in nonlinear feedback control

Abstract

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