The Hopf Algebra of Fliess Operators and Its Dual Pre-lie Algebra

We study the Hopf algebra H of Fliess operators coming from Control Theory in the one-dimensional case. We prove that it admits a graded, finite-dimensional, connected grading. Dually, the vector space ℝ ⟨ x 0, x 1 ⟩ is both a pre-Lie algebra for the pre-Lie product dual of the coproduct of H, and a... View More