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

By T. Oguchi, A. Watanabe, T. Nakamizo. 2002

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Input‐output linearization with delay cancellation for nonlinear delay systems: the problem of the internal stability (2003, background): “The concept of relative degree for nonlinear delay systems was introduced independently in [5,7,10,13], with little differences.”
The Liapunov's second method for continuous time difference equations (2003, methodology): “For instance, if the first equation in (50) is substituted by ’ x1ðtÞ 1⁄4 x2ðtÞ ð0:5þ eÞð1þ x1ðtÞÞx2ðt D1Þ 0:5x q 2ðt D2Þ with e any positive real, then the feedback control law obtained by the methodology in References [4,6] would give, in the case q 1⁄4 1; an unstable internal dynamics.”