English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The goal of the paper is multi-fold. First, an explicit formula is derived tocompute the non-commutative generating series of a closed-loop system when a(multi-input, multi-output) plant, given in Chen--Fliess series description isin multiplicative output feedback interconnection with another system, alsogiven as Chen--Fliess series. Furthermore, it is shown that the multiplicativedynamic output feedback connection has a natural interpretation as atransformation group acting on the plant. A computational framework forcomputing the generating series for multiplicative dynamic output feedback isdevised utilizing the Hopf algebras of the coordinate functions correspondingto the shuffle group and the multiplicative feedback group. The pre--Liealgebra in multiplicative feedback is shown to be an example of Foissy'scom-pre-Lie algebras indexed by matrices with certain structure.

A Formal Power Series Approach to Multiplicative Dynamic Feedback Interconnection