Immersion of nonlinear systems comprising holonomic functions

Abstract

This paper proposes a model simplification method for nonlinear systems comprising holonomic functions. A holonomic function is a nonlinear function that can be associated with a set of partial differential equations called a Pfaffian system, which contains only rational functions in the variable. By considering the Pfaffian system satisfied by all the holonomic functions in the original nonlinear system, it can be extended to another nonlinear system comprising only rational functions in a new state. This conversion of nonlinear systems can be shown to be an immersion, which preserves the input-output map of the original nonlinear system.