Existence and uniqueness of minimal realizations of nonlinear systems

In the theory of finite dimensional linear systems, it is well known that every input-output map that can be realized by one such system can also be realized by a system which is “minimal”, i.e. both controllable and observable. Moreover, the minimal realization of a given map is unique up to isomorphism. It is shown here that similar results hold for the class of all systems whose state space is a real analytic manifold, whose dynamics is given by a family of complete real analytic vector fields, and whose output is an arbitrary real analytic function on the state space.

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