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Enabling analysis of non-linear systems in linear form, the Koopman operator has been shown to be a powerful tool for system identification and controller design. However, current data-driven methods cannot provide quantification of model uncertainty given the learnt model. This work proposes a probabilistic Koopman operator model based on Gaussian processes which extends the author’s previous results and gives a quantification of model uncertainty. The proposed probabilistic model enables efficient propagation of uncertainty in feature space which allows efficient stochastic/robust controller design. The proposed probabilistic model is tested by learning stable nonlinear dynamics generating hand-written characters and by robust controller design of a bilinear DC motor.