38 citations · 95 across the 6 of their papers we have counts for
6 papers
Post-Lie Algebras, Factorization Theorems and Isospectral-Flows
Kurusch Ebrahimi-Fard, Igor Mencattini
In these notes we review and further explore the Lie enveloping algebra of a post-Lie algebra. From a Hopf algebra point of view, one of the central results, which will be recalled…
Discrete-Time Approximations of Fliess Operators
W. Steven Gray, Luis A. Duffaut Espinosa, Kurusch Ebrahimi-Fard
A convenient way to represent a nonlinear input-output system in control theory is via a Chen-Fliess functional expansion or Fliess operator. The general goal of this paper is to d…
Center problem, Abel equation and the Faa di Bruno Hopf algebra for output feedback
Kurusch Ebrahimi-Fard, W. Steven Gray
A combinatorial interpretation is given of Devlin's word problem underlying the classical center-focus problem of Poincare for non-autonomous differential equations. It turns out t…
Dendriform-Tree Setting for Fully Non-commutative Fliess Operators
Luis A. Duffaut Espinosa, W. Steven Gray, Kurusch Ebrahimi-Fard
This paper provides a dendriform-tree setting for Fliess operators with matrix-valued inputs. This class of analytic nonlinear input-output systems is convenient, for example, in q…
A combinatorial Hopf algebra for nonlinear output feedback control systems
Luis A. Duffaut Espinosa, Kurusch Ebrahimi-Fard, W. Steven Gray
In this work a combinatorial description is provided of a Faa di Bruno type Hopf algebra which naturally appears in the context of Fliess operators in nonlinear feedback control th…
Faa di Bruno Hopf Algebra of the Output Feedback Group for Multivariable Fliess Operators
W. Steven Gray, Luis A. Duffaut Espinosa, Kurusch Ebrahimi-Fard
Given two nonlinear input-output systems written in terms of Chen-Fliess functional expansions, it is known that the feedback interconnected system is always well defined and in th…