On the static analysis of nonlinear feedback loops (Q1068742)

This paper deals with the stationary states, or operating points, of simple feedback loops consisting of an arbitrary number of nonlinear subsystems. It is assumed that (1) the static input-output relationship of each subsystem is known; (2) little or nothing is known about their dynamics. The analysis results in (1) a graphical construction of the stationary point, or points, of the system; (2) a simple criterion for the asymptotic stability of each stationary point for those feedback loops where each subsystem in the loop has a one-dimensional state space; (3) a graphical construction for the way in which the operating point is affected by external inputs of the system. A key role in the analysis is played by the (static) open-loop characteristic, a nonlinear analogue of the open-loop gain for linear systems.