On Structural Non-commutativity in Affine Feedback of SISO Nonlinear Systems
<|reference_start|>On Structural Non-commutativity in Affine Feedback of SISO Nonlinear Systems: The affine feedback connection of SISO nonlinear systems modeled by Chen--Fliess series is shown to be a group action on the plant which is isomorphic to the semi-direct product of shuffle and additive group of non-commutative formal power series. The additive and multiplicative feedback loops in an affine feedback connection are thus proven to be structurally non-commutative. A flip in the order of these loops results in a net additive feedback loop.<|reference_end|>
@article{s.2024on,
    title={On Structural Non-commutativity in Affine Feedback of SISO Nonlinear
  Systems},
    author={Venkatesh G. S.},
    journal={arXiv preprint arXiv:2403.17730},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.17730},
    primaryClass={math.OC cs.SY eess.SY}
}