Robust State-Estimation for Fractional-Order Liouvillian Systems

The present article tackles the problem of the estimation of the state variables of fractional-order Liouvillian chaotic systems in the presence of noise. The particular system is presented in the canonical form and fulfills the fractional algebraic observability for a given output of the system. The proposed methodology is structured as follows: given an output signal corrupted by uncertainty, we estimate several fractional-order derivatives of such signal employing a proposed nα-differentiator which is designed by an observer-based sliding-mode control, then by forming a function that depends on the output and its fractional-order derivatives we estimate the states of a chaotic system successfully.