Nonlinear system invariants with applications to identification

The realization theory of stationary linear analytic systems is investigated by means of a class of invariants known as the exceptional points. Concepts like Carleman linearization, multivariable Laplace transform, and semi-lattice are discussed to prepare for the main theorem which characterizes the degree of minimal realization in terms of the minimal generators of the exceptional points. The results here lay the foundation for further work in the realization problem of stationary linear analytic systems. These ideas also have potential application to nonlinear identification and parameter estimation problems.