When classical nonlinear time-delay state-space systems admit an input-output equation of neutral type

This paper deals with nonlinear retarded time-delay systems that surprisingly admit an input-output representation of neutral type. It is shown that such an unexpected behaviour represents a strictly nonlinear phenomenon, for it cannot happen in the linear time-delay case where retarded systems always admit an input-output representation of retarded type. A necessary and sufficient condition under which the nonlinear systems admit a neutral input-output representation is given and strategies for finding an input-output representation of retarded type are briefly outlined. Some open problems that arise, like minimality and system transformations, are discussed as well.