Non-Recursive Fixed-Time Convergence Observer and Extended State Observer

In this paper, non-recursive fixed-time convergence (FxTC) observers were proposed to deal with missions, such as state estimation and tracking differentiation. The observers were designed based on the time-scale paradigm, such that the parameters tuning process could be greatly simplified. The FxTC observers have fast convergence rate, and the convergence time is uniformly bounded by a fixed constant independent of the initial observation errors. Based on the extended state idea, the FxTC observers were redesigned into extended state observers for total disturbance estimation. Some practical rules of thumb were also presented to dispose of the big overshoot of observers' states. Numerical simulations were carried out to verify the feasibility of the observers and the extended state observers.