On Implicit Discretization of Prescribed-Time Differentiator

An implicit Euler discretization scheme of the prescribed-time converging observer from [1] for a second order system is given, which preserves all main properties of the continuous-time counterpart, and can be recursively applied on any interval of time. In addition, the estimation error stays bounded in the presence of bounded measurement noise. The efficiency of the suggested differentiator is illustrated through numeric experiments.