On the stabilization of nonlinear systems

We extend the applicability of the global Q-parametrization method of controller design to a large class of unstable nonlinear plants. The main result is a two-step compensation theorem analogous to that of Zames for unstable linear plants - if P:Le2 → Le1 is a nonlinear (possibly unstable) plant and Fo is any incrementally stable controller such that P1:= P(I-Fo(-P))-1 is incrementally stable, then the class of controllers F which yield a f.g. stable closed-loop system in the unity feedback configuration for P, is globally parametrized by finite gain stable maps Q: Li1 → Le2 with F = Fo + Q(I-P1Q)-1.