Solving the Diophantine equation by state space inversion techniques: an illustrative example

We propose a synthesis procedure for solving the Diophantine equation in the Factorization Approach, based on state space inversion techniques. This new approach is interesting because it allows to extend the powerful factorization approach to the state space one, from a geometric point of view and opens the way towards more general classes of systems, e.g., nonlinear systems ones for which the transfer function setting is not valid but for which the geometric approach exists. In order to clarify the main ideas, we limit the presentation here to a simple illustrative example