Implementation of Discrete-Time Fractional-Order Controllers based on LS Approximations

In this paper we develop rational discrete-time approximations (IIR filters) tocontinuous fractional-order integrators and differentiators of type sα, α ∈ . For that, it isproposed the adoption of the techniques of Padé, Prony and Shanks usually applied in thesignal modelling of deterministic signals. These methods yield suboptimal solutions to theproblem which only requires finding the solution of a set of linear equations. The resultsreveal that this approach gives similar or superior approximations in comparison withother widely used methods. Their effectiveness is illustrated, both in the time and frequencydomains, through several examples.