Coordinates transformations in nonlinear time-delay systems

When considering nonlinear time delay systems, the definition of an invertible change of coordinates is no more granted. Starting from a set of n - 1 exact differentials independent over K(δ] in the variables x(t), ..., x(t-sD), with D a constant commensurate delay and x an n dimensional variable, we give necessary and sufficient conditions for the existence of an exact one-form such that to get a basis for spanK(δ]{dx[0]}.

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