Design of a prescribed convergence time uniform Robust Exact Observer in the presence of measurement noise

In practice, any observer is expected to have small convergence time and high precision despite the presence of disturbances. Decreasing the convergence time usually requires to increase the overall gain of the observer. However, this also amplifies the effect of the noise and deteriorates the precision. This trade-off is studied in this paper for the Uniform Robust Exact Observer for mechanical systems: an observer with uniform convergence with respect to the initial condition. In addition, a method to compute its gains is presented guaranteeing a prescribed convergence time while keeping the best possible precision under measurement noise. A simulation example comparing the performance of the uniform observer with respect to a linear one is presented.