Shift operators and state-affine system theory

Abstract

Using a transform representation, a state-affine realization theory for a Volterra series input-output map is presented. The approach involves the definition of certain shift operators on linear spaces associated with the transforms of the kernals in the Volterra series. The result is a realization algorithm that is extremely easy to implement. The approach also yields a theory of minimality, span-reachability, and observability for infinite degree state-affine systems.