Distinguishability of Discrete-time Nonlinear Systems

This note considers the problem of identifying a discrete-time nonlinear system, within a finite family of possible models, from data sequences of a finite length. The problem is approached by resorting to the notion of output distinguishability. This amounts to asking whether output data sequences generated by different models can be distinguished from one another. A number of results are presented with examples. Connections with conditions for linear systems are established.