Dendriform-Tree Setting for Fully Non-commutative Fliess Operators

TL;DR

This paper introduces a dendriform-tree framework for representing and analyzing matrix-valued Fliess operators, which are useful in quantum control, including convergence conditions for their series representations.

Contribution

It develops a novel dendriform-tree approach to describe non-commutative Fliess operators with matrix inputs, expanding tools for quantum control systems analysis.

Findings

Provides a dendriform-tree representation for Fliess operators

Establishes convergence conditions for the series

Applicable to quantum control systems

Abstract

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.