Nonlinear versus linear control

This chapter considers stabilization problems for uncertain linear systems containing unstructured or structured uncertainty described by integral quadratic constraints. In these problems, we will be interested in the question of whether any advantage can be obtained via the use of a nonlinear controller as opposed to a linear controller. This question is of interest since if no advantage can be obtained via the use of nonlinear controller, then there can be little motivation for the use of a complicated nonlinear controller such as adaptive controller.