When retarded nonlinear time-delay systems admit an input–output representation of neutral type

The paper shows that nonlinear retarded time-delay systems can admit an input–output representation of neutral type. This 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 for a nonlinear system to exhibit this behaviour is given, and a strategy for finding an input–output representation of retarded type is outlined. Some open problems that arise consequently are discussed as well. All the systems considered in this work are time-invariant and have commensurable delays.