Linearization of Input-Output Mapping for Nonlinear Delay Systems via Static State Feedback

The problem of controlling systems described by differential equations with delay in the state is investigated in this paper. The main difficulty in dealing with such delay systems is that the state should be properly considered in an infinite dimensional space. While linear delay systems have been extensively studied in literature, few attention has been devoted to nonlinear delay systems, due to the mathematical difficulties derived by the infinite dimensionality of the state and by the nonlinear structure of the differential equations. In this paper, through the use of a suitable formalism, we show a solution of the problem of the input-output linearization via static-state feedback for an interesting class of nonlinear delay systems. Simulation results on an unstable nonlinear delay system are reported.