State Estimation for a Class of Fractional-Order Linear Systems by the Generalized Modulating Functions Method

This paper investigates a new way of estimating the state of a class of fractional-order linear systems. Based on the generalized modulating functions method, the proposed estimator is non-asymptotic and robust against noises. First, the system is transformed into the observable normal form before being converted into the input-output differential equation, on which the generalized modulating functions method is applied. Then, the state variables are obtained by calculating a group of initial values and output integrals, which are all provided by algebraic integral formulas. Finally, to illustrate the performance of the proposed method, a numerical simulation example is provided.