Input-output feedback linearization of time-delay systems

In this note, the input-output linearization problem (IOLP) for a class of single-input-single-output nonlinear systems with multiple delays in the input, the output, and the state is studied. The problem is solved by means of various static or dynamic compensators, including state and output feedback. The mathematical setting is based on some noncommutative algebraic tools and the introduction of a nonlinear version of the so-called Roesser models for this class of systems. These are claimed to be the cornerstones for studying nonlinear time-delay systems. Necessary and sufficient conditions are given for the existence of a static or pure shift output feedback which solves the IOLP. Sufficient conditions for the existence of a dynamic state feedback solution are included as well.