Factorizations of Nonlinear Systems

Abstract

In this chapter we apply the dissipativity concepts from Chapter 3, in particular the L 2-gain techniques, to obtain some useful types of representations of nonlinear systems, different from the input-state-output representation. In Section 6.1 we will derive stable kernel and stable image representations of nonlinear systems, and we will use them in order to formulate nonlinear perturbation models (with L 2-gain bounded uncertainties). In Section 6.2 we will employ stable kernel representations in order to derive a parametrization of stabilizing controllers, analogous to the Youla-Kucera parametrization in the linear case. Finally, in Section 6.3 we consider the factorization of nonlinear systems into a series interconnection of a, for instance, minimum phase system and an inner system which preserves the L 2-norm.KeywordsNonlinear SystemOptimal Control ProblemImage RepresentationMinimum PhaseInternal Model ControlThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.