Dynamic extension is useful in the design of observers for non linear systems. The idea is to immerse the given system dynamic into a bigger one having a structure more appropriate for building an observer. The main drawback of such a procedure is the need for inverting on-line an injective immersion. In this work we suggest a solution to overcome this difficulty based on an extension of the initial state space. One of the two crucial steps of our approach is the problem of continuous completion of a full column-rank matrix into an invertible one. 53rd IEEE Conference on Decision and Control