Nonlinear operators of system analysis
G. Zames · 1960
In this report the method of functional iteration is introduced as a means for solving nonlinear feedback equations. It is applied to a variety of feedback problems. Equations of feedback systems are written in terms of an operator algebra extracted from functional analysis and solved by geometric iteration. This method leads to a means of bounding the output in terms of the system loop gain, and to a procedure for synthesizing systems out of iterative physical structures. The theory is applied to the construction of an explicit model for the nonlinear distortion of a feedback amplifier, and to the proof of a theorem that states that a bandlimited signal having the width of its spectrum expanded by an invertible, nonlinear, no-memory filter can be recovered from only that part of the filtered signal which lies within the original passband; a filter for recovering the original signal is derived. An exponential iteration is introduced and applied to the study of the realizability of nonlinear feedback systems. A condition, related to certain unavoidable properties of inertia and storage, is found. Models of physical systems satisfying this condition always lead to realizable solutions in feedback problems, and