Abstract
The main objective of this paper is to describe a class of functional series expansions, known as Fliess operators, which admit inputs from a ball in an L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> space as well as Poisson random processes. It is shown that a continuous-time switched input-affine nonlinear system with a Poisson switching signal can be represented as a Fliess operator, and that the underlying combinatorics can be used to obtain, for certain cases, a closed-form solution in terms of Poisson integrals.
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