Functional series expansions for continuous-time switched systems

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_ρ 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.