Modelling and initialization of fractional order nonlinear systems: the infinite state approach

Abstract

In this paper, we generalize the infinite state representation to the modeling of fractional order nonlinear differential systems. This technique is based on the infinite dimension modal model of the fractional integrator whose internal frequency distributed state defines the nonlinear fractional differential systems (FDS) state. Thanks to numerical simulations, we demonstrate that system dynamical behaviors are dependant on infinite dimension distributed initial conditions. Moreover, we show that these initial conditions have a direct consequence on system stability.