On the state-space modeling of fractional systems

This paper presents a method to develop an equivalent fractional state-space model to an integer-order one. Under proper choice of initial conditions, the two systems exhibit similar impulse response. The proposed modeling methods can be generalized to generate a wide range of fractional-order state-space models from their integer-order counterpart. It will be shown via simple examples that proper modeling depends on the selection of the initial conditions of the intermediate virtual fractional state dynamics, which depends on the sampling interval.