In this article, the problem of observer design in linear multi-output systems with asynchronous sampling is addressed. The proposed multi-rate observer is based on a continuous-time Luenberger observer design coupled with an inter-sample predictor for each sampled measurement, which generates an estimate of the output in between consecutive measurements. The sampling times are not necessarily uniformly spaced, but there exists a maximum sampling period among all the sensors. Sufficient and explicit conditions are derived to guarantee exponential stability of the multi-rate observer. The proposed framework of multi-rate observer design is examined through a mathematical example and a gas-phase polyethylene reactor. In the latter case, the amount of active catalyst sites is estimated, with a convergence rate that is comparable to the case of continuous measurements. (C) 2017 American Institute of Chemical Engineers