Input-output linearization of retarded non-linear systems by using an extension of Lie derivative

This paper considers the input-output linearization problem for retarded non-linear systems, which have time-delays in the state. By using an extension of the Lie derivative for functional differential equations, we derive a coordinates transformation and a static state feedback to obtain linear input-output behaviour for a class of retarded non-linear systems. The obtained coordinates transformation is allowed to contain not only the current value of the state variables but also the past values of ones. In addition, we show that the coordinates transformation is invertible in a neighbourhood of the origin and examine the stability condition of the closed loop system with the static state feedback. The effectiveness of the proposed technique is demonstrated through numerical simulations.