REALIZATION AND MINIMAL ORDER FOR NONLINEAR SYSTEMS

The realization problems for single input/single output differential equations are discussed within the framework of differential vector space.Main results of this work answer two fundamental questions:(1) under what conditions different input/output differential equations have the same realization;(2)how to calculate the order of the minimal realization of input/output differential equations without knowing its realization.In order to solve these problems the notion of transfer function for nonlinear systems is defined over a non commutative polynomial ring.The description of nonlinear realization problems is fully incorporated with that of the linear control theory.