A new modulating functions method for state estimation of integer order system

In this paper, a new modulating functions method is proposed to non-asymptotically and robustly estimate the state and its fractional derivative for a class of integer order linear systems in noisy environment. For this purpose, the considered system modeled by the state space representation is firstly transformed into the observable canonical form. Secondly, based on that, the new modulating functions method is applied to obtain algebraic integral formulas for the state and its fractional derivative. These integral formulas can give robust estimations in discrete noisy cases. Furthermore, it is shown how to design the required modulating functions. To demonstrate the efficiency and advantages of the proposed method, one numerical example is given by comparing with a Luenberger observer.