Algebraic Estimation Method of Multiple Disturbances for a Class of Fractional Order Linear Systems*

A novel algebraic method is designed in this paper to estimate the matched multiple disturbances for a class of fractional order linear systems. For the potential application of active anti-disturbance control, the estimations given by the proposed method are accurate and robust against measurement noises. First, the studied system is formulated with matched multiple disturbances. Second, thanks to an auxiliary vector function, algebraic integral formulas are derived to algebraically give the multiple disturbances in a vector-matrix form without computing the derivatives of the pseudo-state and the input. Finally, simulation results are provided to verify the efficiency of the proposed method in noisy environment.