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Hankel Operators for Fractional-Order Systems

Adams, Jay L.
http://rave.ohiolink.edu/etdc/view?acc_num=akron1248198109

Abstract Details

2009, Doctor of Philosophy, University of Akron, Electrical Engineering.
This dissertation presents an algorithm utilizing four unitarily equivalent representations of the Hankel operator to estimate the Hankel singular values of fractional-order systems based on the Rayleigh-Ritz method. This algorithm is applied to estimate the first ten Hankel singular values for systems of the forms s/(s^0.5+1) for real, positive a and 1/(s^q+1) for 0 < q < 2. Error bounds are generated for each Hankel singular value estimate. The algorithm is also applied to two physical fractional-order systems, the resistor-terminated and inductor-terminated semi-infinite lines, to show how it can be used. Hankel norms are also approximated for conjugate-order systems of the form (1/2)/(s^q+1)+(1/2)/(s^q*+1) for a variety of complex q to highlight the flexibility of the algorithm in Hankel-norm computation for a wide variety of systems.
Tom T. Hartley, PhD (Advisor)
Robert J. Veillette, PhD (Advisor)
254 p.
Electrical Engineering
fractional-order calculus; fractional-order systems; Hankel singular values

Recommended Citations

Citations

  • Adams, J. L. (2009). Hankel Operators for Fractional-Order Systems [Doctoral dissertation, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1248198109

    APA Style (7th edition)

  • Adams, Jay. Hankel Operators for Fractional-Order Systems. 2009. University of Akron, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1248198109.

    MLA Style (8th edition)

  • Adams, Jay. "Hankel Operators for Fractional-Order Systems." Doctoral dissertation, University of Akron, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=akron1248198109

    Chicago Manual of Style (17th edition)

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© 2009, all rights reserved.
This open access ETD is published by University of Akron and OhioLINK.