An algorithm for modeling the step response behavior of ground stable nonlinear systems

An algorithm for modeling the step response behavior of ground stable nonlinear devices and systems is presented. The algorithm converges in the mean-square sense to an exact orthogonal representation whenever the nonconstant component of the step response is a finiteenergy signal. Terminating the algorithm after <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> iterations results in an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> th-order model whose dynamics are segregated from the nonlinearity in the tradition of Wiener. The model admits a simple circuit realization, and the parameters which characterize it. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N + I</tex> nonlinear functions of a single variable, can all be obtained directly from terminal measurements. Three examples are cited, and a class of nonlinear differential systems is identified for which the algorithm converges.