Robust estimation of the fractional integral and derivative of the pseudo-state for a class of fractional order linear systems

This paper aims at non-asymptotically estimating the fractional integral and derivative of the pseudo-state for a class of fractional order linear systems in noisy environment with unknown initial conditions. For this purpose, the estimation problem is transformed to estimate the fractional integral and derivative of the output and a set of unknown initial conditions. Then, the modulating functions method is applied to obtain explicit algebraic integral formulae, which give robust estimations in discrete noisy case. Finally, numerical simulations are provided to demonstrate the efficiency of the proposed method.