Equivalence of discrete-time nonlinear systems to prime systems under proper generalized output transformations

The notion of generalized output transformations for discrete-time nonlinear system is introduced and some of its properties are studied. This transformation can be thought of as a generalization to the nonlinear setting of an unimodular transformation in the output space. Within a linear algebraic framework, we present necessary and sufficient conditions for a discrete-time nonlinear system to be equivalent to a prime system under a certain group of transformations that includes generalized output transformation.