On the local convergence of Fliess operators driven by L2-Itô random processes

Fliess operators, which are a type of functional series expansion, have been used to describe a broad class of nonlinear input-output maps driven by deterministic inputs. But in most applications, a system´s inputs have noise components. It has been shown that the notion of a Fliess operator can be generalized to admit a class of L2-Itô stochastic input processes, and that they converge absolutely over an arbitrarily large but finite time interval when a certain coefficient growth condition is met. However, a significant number of systems fail to meet this condition. In this paper, the methodology is extended by considering instead an interval of convergence with a random length. It results in a less restrictive sufficient condition for convergence, and thus, is applicable to a larger class of systems.