Generating Series for Networks of Chen-Fliess Series

Abstract

Consider a set of single-input, single-output nonlinear systems whose input-output maps are described only in terms of convergent Chen-Fliess series without any assumption that finite dimensional state space models are available. It is shown that any additive or multiplicative interconnection of such systems always has a Chen-Fliess series representation that can be computed explicitly in terms of iterated formal Lie derivatives.

Added and updated references, fixed typos

Cited by in corpus (3)

• On expansions for nonlinear systems, error estimates and convergence issues
• Continuity of Formal Power Series Products in Nonlinear Control Theory
• Entropy of Generating Series for Nonlinear Input-Output Systems and Their Interconnections