Dendriform-Tree Setting for Fully Non-commutative Fliess Operators
  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 quantum control. In particular, a description of such Fliess operators is provided using planar binary trees. Sufficient conditions for convergence of the defining series are also given. 
Luis A. Duffaut Espinosa, W. Steven Gray and Kurusch Ebrahimi-Fard
math.CO