The ensemble Kalman filter belongs to the class of iterative particle
filtering methods and can be used for solving control--to--observable inverse
problems. In recent years several continuous limits in the number of iteration
and particles have been performed in order to study properties of the method.
In particular, a one--dimensional linear stability analysis reveals a possible
instability of the solution provided by the continuous--time limit of the
ensemble Kalman filter for inverse problems. In this work we address this issue
by introducing a stabilization of the dynamics which leads to a method with
globally asymptotically stable solutions. We illustrate the performance of the
stabilized version of the ensemble Kalman filter by using test inverse problems
from the literature and comparing it with the classical formulation of the
method
