An innovative fixed-pole numerical approximation for fractional order systems

A novel numerical approximation scheme is proposed for fractional order systems by the concept of identification. An identical equation is derived firstly, from which one can obtain the exact state space model of fractional order systems. It reveals the nature of the approximation problem, and then provides an effective scheme to obtain the desired model. This research project also focuses on solving a knotty but crucial issue, i.e., the initial value problem of fractional order systems. The results generated by the study prove that it can reduce to the Caputo case by selecting some specific initial values. A careful simulation study is reported to illustrate the effectiveness of the proposed scheme. To exhibit the superiority clearly, the results are compared with that of the published fixed-pole finite model method.