Robust commensurate fractional differentiators for a class of fractional order linear systems

A series of robust commensurate fractional differentiators are proposed for a class of fractional order linear systems in this paper. Such differentiators are based on the modulating functions method. First, fractional integration by parts formulas and modulating functions are used to eliminate the undesired terms and keep needed items. Second, a recursive algorithm is designed to calculate the required derivatives. In this way we can get a set of estimation results in one calculation, and it only requires less computational cost. Moreover, a detailed noise error analysis of the algorithm is performed to improve the estimation results. Finally, the efficiency and robustness of the presented method is verified by numerical simulations.