Robust estimation for the fractional integral and derivative of the output for a class of fractional order linear systems

This paper aims at non-asymptotically estimating the fractional integral and derivative of the output for a class of fractional order linear systems in noisy environment with unknown initial conditions. For this purpose, the considered system modeled by the pseudo-state space representation is firstly transformed into a fractional order differential equation. Secondly, based on the obtained equation the modulating functions method is applied to obtain algebraic integral formulae for the desired fractional integral and derivative, where the undesired initial conditions are eliminated. These integral formulae can give robust estimations in discrete noisy cases. Thirdly, it is shown how to construct the used modulating functions. Finally, numerical simulations are provided to demonstrate the efficiency of the proposed method.