The content delves into the structural non-commutativity in the feedback loops of SISO nonlinear systems modeled by Chen-Fliess series. It explores the affine feedback connection, the group actions, and the quantification of non-commutativity between the additive and multiplicative feedback loops. The document provides a detailed analysis of formal power series, bialgebras, and the affine feedback transformation group. It also discusses the composition of Chen-Fliess series, convergence, and Fliess operators. The structural non-commutativity is illustrated through diagrams and mathematical proofs. The content concludes with discussions on Lie algebras, post-groups, and acknowledgments.
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arxiv.org
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