Factorization and feedback stabilization for nonlinear systems

Abstract

We establish the equivalence of internal input-out stability for two feedback configurations of a nonlinear, time-varying plant P for which a related plant G is assumed to have a factorization G = ϑ R with both R and R −1 incrementally stable; this extends a factorization principle for stabilizability previously given only for the linear, time-invariant case. As an application of a special case we recover a version of the Youla parametrization of stabilizing compensators for the nonlinear case previously presented in the literature. We use degree theory to parametrize a collection of solutions of the H ∞-control problem for the case of a 1-gain stable or lossless plant. In the case of a plant G having a J-inner-outer factorization, this last result combined with the above-mentioned factorization principle leads to results on the H ∞-control problem for P.