Loewner Functions for a Class of Nonlinear Differential-Algebraic Systems

We consider the Loewner functions associated to four behaviourally equivalent differential-algebraic systems with the goal of simplifying the partial differential equation (PDE) defining the tangential generalized observability function. Although the systems may have different tangential generalized observability functions, it is shown that all four systems yield the exact same family of Loewner equivalent interpolants provided that solutions to the PDEs exist.