A fractional state space realization method with block pulse basis

In this paper, a new analytic method for the fractional state space modeling of non-integer systems is presented. The tool of orthogonal functions and particularly the block pulse basis is used jointly with their generalized operational matrices in order to establish the state space representation which is not always obvious in the fractional framework. The commensurate case which is the simplest one is firstly handled. Then, the same development is generalized to the non-commensurate case defining so a nonlinear criterion to be minimized. Examples and simulations are presented to show the usefulness of the technique.