Non-asymptotic fractional pseudo-state differentiator for a class of fractional order linear systems

In this paper, a non-asymptotic fractional pseudo-state differentiator is designed for a class of fractional order linear systems in noisy environment. The proposed fractional pseudo-state differentiator is given by the modulating functions method. First, the considered system model is transformed from pseudo-state space representation into a form of fractional differential equation. Second, by successively applying the fractional integration by parts formulas to the integral formulas involving the modulating functions and eliminating the undesired terms, the required fractional derivatives of the output are obtained, where the involved fractional derivative initial values of the output are also estimated in a similar way. Finally, the fractional derivative of the pseudo-state can be obtained by using the ones of the output. Unlike the previous works, the proposed method is no need to require the differentiation order of a system as rational number which will lead to much more computation cost with a larger denominator. Numerical simulations verify the efficiency and robustness of the proposed method.