期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2006
卷号：2006
DOI：10.1155/IJMMS/2006/34217
出版社：Hindawi Publishing Corporation
摘要：The formal Laplace-Borel transform of an analytic integral
operator, known as a Fliess operator, is defined and developed.
Then, in conjunction with the composition product over formal
power series, the formal Laplace-Borel transform is shown to
provide an isomorphism between the semigroup of all Fliess
operators under operator composition and the semigroup of all
locally convergent formal power series under the composition
product. Finally, the formal Laplace-Borel transform is applied in
a systems theory setting to explicitly derive the relationship
between the formal Laplace transform of the input and output
functions of a Fliess operator. This gives a compact
interpretation of the operational calculus of Fliess for computing
the output response of an analytic nonlinear system.
