Analysis of the Use of Low-Pass Filters with High-Gain Observers

High-gain observers play an important role in the design of feedback control for nonlinear systems. One challenge in the use of high-gain observers is the effect of measurement noise. It is shown in the literature that the presence of measurement noise puts a constraint on how high the observer gain could be, which forces a trade-off between the fast convergence of state estimates and the error due to measurement noise. A number of techniques have been proposed in the literature to attenuate the effects of measurement noise on systems utilizing a high-gain observer. In experimental applications of high-gain observers, it is quite common to use a low-pass filter to filter out the high-frequency components of the noise before feeding the measurement into the observer. In this paper we analyze effect of measurement noise on high-gain observers when low pass filters are used.