A generalized power series and its application in the inversion of transfer functions

The paper proposes a new approach to compute the impulse response of fractional order linear time invariant systems. By applying a general approach to decompose a Laplace transform into a Laurent like series, we obtain a power series that generalizes the Taylor and MacLaurin series. The algorithm is applied to the computation of the impulse response of causal linear fractional order systems. In particular for the commensurate case we propose a table to obtain the coefficients of the MacLaurin series. Through what we call the correspondence principle we show that it is possible to obtain a fractional order Laplace transform solution from the integer one. Some examples are presented.