Initial Conditions and Initialization of Fractional Systems

Abstract

In this paper, the initialization of fractional order systems is analyzed. The objective is to prove that the usual pseudostate variable x(t) is unable to predict the future behavior of the system, whereas the infinite dimensional variable z(د‰, t) fulfills the requirements of a true state variable. Two fractional systems, a fractional integrator and a onederivative fractional system, are analyzed with the help of elementary tests and numerical simulations. It is proved that the dynamic behaviors of these two fractional systems differ completely from that of their integer order counterparts. More specifically, initialization of these systems requires knowledge of z(د‰,t0) initial condition.