Prescribed-Time Observer Is Naturally Robust Against Disturbances and Unmodeled Dynamics

This paper addresses the robustness of a prescribed-time observer for a class of nonlinear systems in the presence of disturbances and unmodeled dynamics. It is proven and demonstrated through simulations that the proposed observer completely rejects the effects of arbitrarily large bounded disturbances and unmodeled dynamics, enabling accurate estimation of both the states and the disturbances. Furthermore, a comparison with the standard high-gain observer is provided to highlight the superiority of the prescribed-time observer in reducing the peaking phenomenon and improving estimation accuracy.