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The goal of this paper is to describe the parametric sensitivity functions associated with the left inverse of any single-input, single-output system written in terms of a Chen-Fliess functional series whose generating series has a well defined relative degree. A formula is also given to describe how this sensitivity gets propagated to the output. The technique is demonstrated with an example.
The feedback interconnection of two systems written in terms of Chen-Fliess series can be described explicitly in terms of the antipode of the output feedback Hopf algebra. At present, there are four known computational approaches to calculating this antipode. The main goal of this paper is to compare the computational performances of the three latest methods, two coproduct recursion methods and the...
Given two nonlinear input–output systems written in terms of Chen–Fliess functional expansions, i.e., Fliess operators, it is known that the feedback interconnected system is always well defined and in the same class. An explicit formula for the generating series of a single-input, single-output closed-loop system was provided by the first two authors in earlier work via Hopf algebra methods. This...
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