The electrooculography (EOG) signal is considered most suitable for drowsiness detection. Besides its simplicity and low cost, EOG signals are not affected by environmental factors such as light intensity and driver movement. However, existing EOG-based drowsiness detection techniques employ arbitrarily chosen features for classifier training, leading to results that are less robust against changes in the measurement method, noise level, and individual subject variability. In this study, we propose a system dynamics-based approach to drowsiness detection. The EOG signal is treated as a neurophysiological response of the oculomotor system. Each blink action is considered as a result of a series of neuron firing impulses entering the system. Blink signatures are thus extracted to identify the system transfer function, from which system poles are computed to characterize the drowsiness state of the subject. It was found that the location of system poles on the pole-zero map for blink signatures from an alert state were distinctly different from those from a drowsy state. A simple criterion was subsequently developed for drowsiness detection by counting the ratio of real and complex poles of the system over any given period of time. The proposed methodology is a systematic approach and does not require extensive classifier training. It is robust against variations in the subject condition, sensor placement, noise level, and blink rate.