Abstract
This paper deals with the design of super-twisting algorithm-based sliding-mode observer for uncertain nonlinear fractional-order system subject to unknown inputs. Fractional-order super-twisting algorithms (FSTA) are proposed for both commensurate and incommensurate fractional-order nonlinear systems. Then, step-by-step sliding-mode observers based on the FSTA are designed. Finite-time convergence and robustness are proven. Finally, application to the synchronization of two fractional-order chaotic systems is given.