Characterizing nonlinear realizations of linear I/O maps

We hypothesize existence of a finite dimensional nonlinear linear analytic realization for a time varying linear i/o functional. From previous work, this implies existence of a minimal linear time-varying realization for this map. From the work of Sussmann, this hypothesis also implies existence of minimal (not necessarily linear) realization of this map. Using an isomorphism theorem of Sussmann, we obtain existence of analytic isomorphism between the two existing minimal realizations.