State estimation based on fractional order sliding mode observer method for a class of uncertain fractional-order nonlinear systems

• Fractional-order SMO structures for FO nonlinear systems are presented.
• Asymptotic stability of error is analyzed via Lyapunov stability analysis method.
• FOSMOs for constant and uncertain-parameter FO nonlinear systems are discussed.
• Multiple simulation examples validate the effectiveness of the designed FOSMOs.

State estimation of dynamic systems is quite significant in many research areas, such as state-based control and stabilization, state-based monitoring and fault detection. This paper is concerned with the problem of observer-based state estimation for a class of fractional-order (FO) nonlinear dynamic systems. The objective is to consider the state estimation of FO nonlinear system with the sliding mode control (SMC) technique, and conduct the asymptotic stability analysis for the estimate error dynamic system. Firstly, the considered FO nonlinear system models with constant and uncertain parameters are both presented. Fractional order sliding mode observer (FOSMO) structures are established for the FO nonlinear system models. Then, the asymptotic stability of the estimate error dynamic systems are analyzed via employing the Lyapunov stability analysis method for FO systems, and the sufficient conditions of asymptotic stability are derived. FOSMOs design for FO nonlinear systems of Caputo׳s and Riemann–Liouville׳s differential operators are both investigated, and the corresponding asymptotic stability sufficient conditions of the error dynamic systems are presented to insure the estimation accuracy of FOSMOs. Finally, multiple simulation examples are provided to demonstrate the effectiveness of the presented FOSMOs.