Non-asymptotic and robust estimation for fractional order pseudo-state space model using an algebraic parametric method

Abstract

This paper mainly investigates the derivative estimation problem for a class of fractional order linear systems. After applying the Laplace transform to the considered pseudo-state space representation model, a series of multiplications and derivations are applied to eliminate unknown initial conditions, which define an annihilator. Then, through strict mathematical derivation, an input-output integral equation is deduced when returning into the time domain. Based on the obtained equation and thanks to the fractional Leibniz formulas, algebraic integral formulas are provided, which can non-asymptotically and robustly estimate the fractional derivatives of the system output. Moreover, error analysis in discrete noisy cases is given to study the performance of the proposed differentiator. Finally, numerical simulations are provided to show the effectiveness of the proposed method.