Hankel-norm estimation for fractional-order systems using the Rayleigh-Ritz method

  • Authors:

  • Jay L. Adams;Tom T. Hartley;Robert J. Veillette

  • Affiliations:

  • Department of Electrical and Computer Engineering, The University of Akron, Akron, OH, 44325-3904, USA;Department of Electrical and Computer Engineering, The University of Akron, Akron, OH, 44325-3904, USA;Department of Electrical and Computer Engineering, The University of Akron, Akron, OH, 44325-3904, USA

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2010

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Abstract

In this paper, the Rayleigh-Ritz method of estimating the eigenvalues of an operator on a Hilbert space is utilized to determine the magnitude of the largest eigenvalue for the Hankel operator of fractional-order systems, the Hankel norm. This provides a measure of the possible retrievable energy from the system in the future compared to the energy that was put into the system in the past. The application of the Rayleigh-Ritz method to obtaining underestimates of the Hankel norm of a fractional-order system is described. Several examples are given, demonstrating the method.