In this paper we present an estimator based on the Euler discretization. First, we show that the proposed estimator is an exponential observer in the case when the error between trajectories of continuous time and its associated Euler discretized system can be neglected. Otherwise, we show that the error of estimation is exponentially attracted by some neighbourhood of the origin which depends only on the sampling time. Finally, numerical simulations using a bioreactor model are given in order to highlight the performance of the proposed estimator.