The formal Laplace-Borel transform of Fliess operators and the composition product
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 Fl...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/34217 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |