Input-output feedback linearization of nonlinear time-delay systems

In this paper, the input-output linearization problem for a class of single-input single-output nonlinear systems with multiple delays in the input 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 so-called Roesser models for this class of systems and on some noncommutative algebraic tools. 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 input-output linearization problem. Sufficient conditions for the existence of a dynamic state feedback solution are included as well.