Identificatin of nonlinear systems with finite settling time by classifying nonlinear element

We investigate the identification problem of the nonlinear systems with the unknown structure. It is well known that the nonlinear systems with the finite settling time may be represented by the nonlinear memoriless part cascaded with the linear memory part. In this papar, let us consider such nonlinear systems and discriminate the structure of these nonlinear part by the following classification. The characteristics of the nonlinear systems may appear in the distribution of the output. That is, the probabilitydensity of the output becomes the delta function at the extremum of the nonlinear fuction and there may be the domain which the probbility density of the output is zero. Therefore, the nonlinear systems may be classified by the number of the peaks of probability density and the intervals on which the probability density is zero. Next, from the candidate systems which are include in the same class, we can determine the structure of the system and estimate its parameters under the quantitative criterion. Furthermore, it is shown by the digital simulation that this identification method is theoretically justified.