arXiv subjects
Publications and source records attributed to Venkatesh G. S..
The main objective of this work is to show that the single-input, single-output (SISO) affine feedback group, a transformation group in the context of the affine feedback interconnection of Chen-Fliess series, is a post-group in the sense of Bai, Guo, Sheng and Tang.
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.