Modulating functions based differentiator of the pseudo-state for a class of fractional order linear systems

In this paper, an algebraic and robust fractional order differentiator is designed for a class of linear systems with arbitrary differentiation in [0,2]. It to estimate the derivative pseudo-state as well one output. particular, it can also pseudo-state. Different from our previous works, considered system no longer relies on matching conditions, which makes model be more general. First, transformed into differential equation space representation. Second, based obtained equation, series equations are constructed by applying different operators. Then, modulating functions method introduced recursively give integral formulas set derivatives output initial values. These used non-asymptotically robustly discrete noisy cases. Third, required designed. After giving associated estimation algorithm, numerical simulation results finally given illustrate accuracy robustness proposed method.