On the equivalence between nonlinear- and fractional bilinear- control systems

Stated in a few word, the aim of this paper is to give evidence to the following author´s conjecture: `any´ nonlinear control system is equivalent to a (larger dimensioned) bilinear fractional differential system. The main purpose is to motivate a new approach in nonlinear control, and for this reason, in this paper, some simple examples, nevertheless yet meaningful, are given, where the above conjecture holds. Starting with a simple scalar example, in order to present the basic feature of the method, the paper is endowed with a case consisting in a two dimensional control system, which is nevertheless amenable to be readily generalized to a general state-space dimension. A subresult of this paper is interesting by itself: for classical polynomial systems, where just positive integers powers are involved, the result holds always, and the equivalent system result in an ordinary (non-fractional) bilinear system.