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

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  • Yaqin Li
  • W. Steven Gray

Abstract

The formal Laplace-Borel transform of an analytic integraloperator, known as a Fliess operator, is defined and developed.Then, in conjunction with the composition product over formalpower series, the formal Laplace-Borel transform is shown toprovide an isomorphism between the semigroup of all Fliessoperators under operator composition and the semigroup of alllocally convergent formal power series under the compositionproduct. Finally, the formal Laplace-Borel transform is applied ina systems theory setting to explicitly derive the relationshipbetween the formal Laplace transform of the input and outputfunctions of a Fliess operator. This gives a compactinterpretation of the operational calculus of Fliess for computingthe output response of an analytic nonlinear system.

Suggested Citation

  • Yaqin Li & W. Steven Gray, 2006. "The formal Laplace-Borel transform of Fliess operators and the composition product," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-14, July.
    • Handle: RePEc:hin:jijmms:034217
    DOI: 10.1155/IJMMS/2006/34217
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