Algorithms for Fractional Dynamical Behaviors Modelling Using Non-Singular Rational Kernels

This paper proposes algorithms to model fractional (dynamical) behaviors using non-singular rational kernels whose interest is first demonstrated on a pure power law function. Two algorithms are then proposed to find a non-singular rational kernel that allows the input-output data to be fitted. The first one derives the impulse response of the modeled system from the data. The second one finds the interlaced poles and zeros of the rational function that fits the impulse response found using the first algorithm. Several applications show the efficiency of the proposed work.