Functional Series Expansions for Continuous-Time Switched Systems

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 p space as well as Poisson random processes. Conditions are given under which these functional series expansions converge absolutely in the mean. Then, 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 for certain cases a closed form solution can be obtained in terms of Poisson integrals.