From nonlinearity to nonlinearizability indices

Meaningful nonlinearity indices have long been recognized as potentially useful tools in many system analysis, or design problems. In this paper, the best known nonlinearity indices are briefly recalled within the framework of a fairly general unifying view. Based on the argument that any I/O feedback linearizable system (nonlinear system which is properly I/O linearizable by (output) feedback) should not, in a sense, be thought of as really nonlinear, the notion of a nonlinearity index is properly extended to that of nonlinearizability index. Both model-based and data-based methods for the computation of nonlinearizability indices are briefly discussed.