Analysis of Sampled-data High-gain Observers in the Presence of Measurement Noise

This paper studies sampled-data output feedback control of nonlinear systems using high-gain observers in the presence of measurement noise. The observer is designed in continuous time, then discretized. It is shown that the sampled-data output feedback controller recovers the performance of the continuous-time state feedback controller as the observer gain is increased. However, the effect of measurement noise dominates beyond a certain point, and the gap between the performance of the two controllers widens as the observer gain is increased further. The analysis quantifies the relationship between the high-gain observer parameter and the amplitude of the noise.