High-order sliding mode observer for fractional commensurate linear systems with unknown input

In this paper, a high-order sliding mode observer (HOSMO) is proposed for the joint estimation of the pseudo-state and the unknown input of fractional commensurate linear systems with single unknown input and a single output. The convergence of the proposed observer is proved using a Lyapunov-based approach. In addition, an enhanced variant of the proposed fractional-HOSMO is introduced to avoid the peaking phenomenon and thus to improve the estimation results in the transient phase. Simulation results are provided to illustrate the performance of the proposed fractional observer in both noise-free and noisy cases. The effect of the observer’s gains on the estimated pseudo-state and unknown input is also discussed.