On Structural Non-commutativity in Affine Feedback of SISO Nonlinear Systems
Optimization and Control
2024-03-27 v1 Systems and Control
Systems and Control
Abstract
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.
Cite
@article{arxiv.2403.17730,
title = {On Structural Non-commutativity in Affine Feedback of SISO Nonlinear Systems},
author = {Venkatesh G. S.},
journal= {arXiv preprint arXiv:2403.17730},
year = {2024}
}
Comments
submitted to $26^{th}$ International Symposium on Mathematical Theory of Networks and Systems, 2024