Disclosing and overcoming inexact nonlinearity cancellation issues

A natural way of controlling linear systems feedback interconnected with memoryless nonlinearities is canceling this latter with a first feedback loop, and then designing a linear controller for the remaining linear dynamics. Nevertheless, this procedure may provide unsatisfactory performance, and even lead to instability, when the nonlinearity can not be exactly cancelled due to lack of information or limitations on the nonlinear approximation. In this paper the interplay between the robustness with respect to state estimation and the quality of the approximation of the nonlinearity is investigated and on such insights an alternative approach guaranteeing sufficient conditions for the stability is derived. A comparison with standard methods on a benchmark system shows that taking explicitly into account such an interplay leads to less conservative solutions.