Modelling and simulation of nabla fractional order systems using vector fitting method.

The paper focuses on the numerical approximation of discrete fractional order systems. First of all, an infinite dimensional frequency distribution model of discrete fractional order system is given. Then, resorting the nabla discrete Laplace transform, the rationality of the finite dimensional frequency distribution model approaching the infinite one is illustrated. Based on this, an original algorithm to estimate the parameters of the approximate model is proposed with the help of vector fitting method. What is more, this approximation method is extended to the approximation of the general discrete fractional order systems. Numerical examples are carried out to show the applicability and flexibility of the introduced methodology.