Some input-output properties of nonlinear multivariable feedback systems

This short paper presents a number of results which characterize the input-output response of a class of nonlinear multivariable systems. A rather general class of nonlinear multivariable systems is considered and a variety of input functions is allowed. Particular conditions are developed which guarantee that the error between the input function and the output response 1) is bounded, 2) tends to a constant value, and 3) tends to zero. The results are of special interest since they can be interpreted as defining a limited form of "superposition principle" for the nonlinear systems considered.