On retarded nonlinear time-delay systems that generate neutral input-output equations

In this work retarded nonlinear time-delay systems that surprisingly admit an input-output representation of neutral type are discussed. It is shown that such a behaviour is a strictly nonlinear phenomenon, as it cannot happen in the linear time-delay case where the input-output representation of retarded systems is always of retarded type. A necessary and sufficient condition under which nonlinear systems admit a neutral input-output representation is given. Some open problems, like minimality and system transformations, are discussed as well.