Orthonormal basis functions for modeling continuous-time fractional systems

Abstract

The classical Laguerre functions are known to be divergent as soon as their differentiation order is non-integer. They are hence inappropriate for representing fractional differentiation systems. A complete orthogonal basis, having fractional differentiation orders and a single pole, is synthesized. It extends the well-known definition of Laguerre functions to fractional systems. Hence a new class of fixed denominator models is provided for system identification. Fourier coefficients are computed using a least squares method. The least squares error is plotted versus the differentiation order and the pole, in an example, and shows that an optimal differentiation order may be located away from an integer number. Hence, the use of the synthesized basis is fully justitied.