Sampling Zeros of Discrete Models for Fractional Order Systems

Most real systems evolve in continuous-time and are modeled using differential equations. However, (discrete-time) sampled-data models are necessary to describe the interaction with digital devices. For rational transfer functions, with integer-order derivatives, a well known consequence of the sampling process is the presence of sampling zeros. In this note we extend this result to systems described in terms of fractional-order derivatives. Specifically we define fractional-order Euler-Frobenius polynomials and we use them to characterize the asymptotic sampling zeros for fractional systems as the sampling period tends to zero.