Fractional state variable filter for system identification by fractional model

This article deals with modeling and identification of fractional systems in the time domain. Fractional state-space representation is defined, and a stability condition for fractional systems given. A new identification method for fractional systems is then proposed. The method is based on the generalization to fractional orders of classical methods based on State Variable Filters (SVF). A particular case of fractional SVF, fractional Poisson filters, is studied. Parameter estimation is then performed, through the conventional least squares method, and then through the instrumental variable method which permits unbiased parameter estimation. Monte Carlo simulations are then performed, using various noise levels, to compare the identification performance of these two methods, and of a prediction error method based on a fractional ARX model.