Order of discrete time nonlinear systems determined from input-output signals

A nonparametric method for the estimation of the order of nonlinear discrete-time systems is given. It proceeds by linearization about different operating points and by the estimation of the order of the linear systems by singular value decomposition. As input signals, white noise is added to a constant that fixes the operating point. Sufficiently small amplitude of the white noise assures that the nonlinear system acts approximately as a linearized system around the operating point. A small amplitude also leads to a low signal-to-noise ratio in the presence of measurement errors. This tradeoff is discussed quantitatively and illustrated by an example. The effect of residual nonlinearity and measurement errors is a possible underestimation of the system order