The formal Laplace--Borel transform of Fliess operators and the composition product (Q885581)

In the paper, the formal Laplace--Borel transform of a Fliess operator is defined and developed. This concept provides an isomorphism between the semigroup of all Fliess operators under composition and the semigroup of all locally convergent formal power series under the composition product. As an application in systems theory, an explicit relationship is derived between the formal Laplace--Borel transforms of the input and output functions of a Fliess operator, which is a compact interpretation of the operational calculus of Fliess.