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

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.