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...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/34217 |
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| _version_ | 1832549879824515072 |
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| author | Yaqin Li W. Steven Gray |
| author_facet | Yaqin Li W. Steven Gray |
| author_sort | Yaqin Li |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b7c46c5de8664086ada53ad5ad7ade00 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b7c46c5de8664086ada53ad5ad7ade002025-02-03T06:08:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/3421734217The formal Laplace-Borel transform of Fliess operators and the composition productYaqin Li0W. Steven Gray1Department of Electrical and Computer Engineering, University of Memphis, Memphis 38152, TN, USADepartment of Electrical and Computer Engineering, Old Dominion University, Norfolk 23529, VA, USAThe 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.http://dx.doi.org/10.1155/IJMMS/2006/34217 |
| spellingShingle | Yaqin Li W. Steven Gray The formal Laplace-Borel transform of Fliess operators and the composition product International Journal of Mathematics and Mathematical Sciences |
| title | The formal Laplace-Borel transform of Fliess operators
and the composition product |
| title_full | The formal Laplace-Borel transform of Fliess operators
and the composition product |
| title_fullStr | The formal Laplace-Borel transform of Fliess operators
and the composition product |
| title_full_unstemmed | The formal Laplace-Borel transform of Fliess operators
and the composition product |
| title_short | The formal Laplace-Borel transform of Fliess operators
and the composition product |
| title_sort | formal laplace borel transform of fliess operators and the composition product |
| url | http://dx.doi.org/10.1155/IJMMS/2006/34217 |
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