Local Nash Realizations

In this paper we investigate realization theory of a class of non-linear systems, called Nash systems. Nash systems are non-linear systems whose vector fields and readout maps are analytic semi-algebraic functions. In this paper we will present a characterization of minimality in terms of observability and reachability and show that minimal Nash systems are isomorphic. The results are local in nature, i.e. they hold only for small time intervals. The hope is that the presented results can be extended to hold globally.