Functional Analysis Applied to Nonlinear Feedback Systems

An operator theory is outlined for the general, nonlinear, feedback loop. Methods for bounding system responses and investigating stability are introduced. An iterative expansion of the feedback loop, valid for large nonlinearities and unstable systems, is derived. The theory is applied to the study of nonlinear distortion in a class of amplifiers; it is shown that feedback reduces distortion for band-limited inputs. A model of the distortion is obtained, shown to be stable, and an iteration whose rate of convergence is optimized is derived.