Modulating functions based state estimator for fractional-order descriptor linear systems

In this paper, the aim is to non-asymptotically and robustly estimate the state for fractional-order descriptor linear systems in a noisy environment. First, the considered fractional-order descriptor systems are transformed into the fractional-order Brunovsky’s observable canonical forms. Second, the considered observable canonical forms are transformed by taking a fractional derivative operator. Third, based on the new forms, algebraic formulas are obtained for the state variables by applying the modulating functions method without knowing the initial condition of systems, despite the corrupting noises are presented in the output measurement. Finally, numerical simulations are given to illustrate the efficiency and robustness of the proposed estimator by comparing with the fractional-order Luenberger-like observer.