The differential field associated to a general analytic nonlinear dynamical system

A rigorous and detailed construction of the differential field K _Σ⟨u,y⟩ associated, in a differential-algebraic context, to a nonlinear system Σ described in state-space form with analytic coefficients is presented. The field K_Σ⟨u,y⟩ represents an input-output description of Σ, and its study is of key importance in problems concerning the input-output behavior of Σ. Technically, the basic step of the construction of K_Σ⟨u,y⟩ consists in proving that the differential ideal associated to the state-evolution equation of Σ is prime