On Volterra expansions for time-varying nonlinear systems

We extend in an important direction recent results by this writer which show for the first time the existence of a locally convergent Volterra series representation for the input-output relation of a certain large class of nonlinear systems containing an arbitrary finite number of nonlinear elements. (Systems of the type considered arise, for example, in the area of communication system modeling.) The extension covers cases in which the linear part of the system is of a more general type that arises often, and unavoidably leads to considerably more complicated general expressions for the terms in the corresponding series expansions.