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On Structural Non-commutativity in Affine Feedback of SISO Nonlinear Systems (2403.17730v1)
Published 26 Mar 2024 in math.OC, cs.SY, and eess.SY
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.
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