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International Journal of Mathematics and Mathematical Sciences
Volume 2006, Article ID 34217, 14 pages
http://dx.doi.org/10.1155/IJMMS/2006/34217

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

1Department of Electrical and Computer Engineering, University of Memphis, Memphis 38152, TN, USA
2Department of Electrical and Computer Engineering, Old Dominion University, Norfolk 23529, VA, USA

Received 28 July 2005; Revised 14 April 2006; Accepted 25 April 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [13 citations]

The following is the list of published articles that have cited the current article.

  • Luis A. Duffaut Espinosa, W. Steven Gray, and Oscar R. González, “On the bilinearity of cascaded bilinear systems,” Proceedings of the IEEE Conference on Decision and Control, pp. 5581–5587, 2007. View at Publisher · View at Google Scholar
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  • Gray, and Wang, “Non-causal Fliess operators and their shuffle algebra,” International Journal of Control, vol. 81, no. 3, pp. 344–357, 2008. View at Publisher · View at Google Scholar
  • W. Steven Gray, Heber Herencia-Zapana, Luis A. Duffaut Espinosa, and Oscar R. González, “On cascades of bilinear systems and generating series of weighted petri nets,” Proceedings of the IEEE Conference on Decision and Control, pp. 4115–4120, 2008. View at Publisher · View at Google Scholar
  • Eric Gehrig, and Matthias Kawski, “A hopf-algebraic formula for compositions of noncommuting flows,” Proceedings of the IEEE Conference on Decision and Control, pp. 1569–1574, 2008. View at Publisher · View at Google Scholar
  • W. Steven Gray, Heber Herencia-Zapana, Luis A. Duffaut Espinosa, and Oscar R. González, “Bilinear system interconnections and generating series of weighted Petri nets,” Systems & Control Letters, vol. 58, no. 12, pp. 841–848, 2009. View at Publisher · View at Google Scholar
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  • Makhin Thitsa, and W. Steven Gray, “On the radius of convergence of cascaded analytic nonlinear systems: The SISO case,” Proceedings of the Annual Southeastern Symposium on System Theory, pp. 30–36, 2011. View at Publisher · View at Google Scholar
  • W.S. Gray, and M. Thitsa, “A unified approach to generating series for mixed cascades of analytic nonlinear input–output systems,” International Journal of Control, vol. 85, no. 11, pp. 1737–1754, 2012. View at Publisher · View at Google Scholar
  • Makhin Thitsa, and W. Steven Gray, “On the radius of convergence of interconnected analytic nonlinear input-output systems,” SIAM Journal on Control and Optimization, vol. 50, no. 5, pp. 2786–2813, 2012. View at Publisher · View at Google Scholar