Stubborn ISS Redesign for Nonlinear High-Gain Observers

We propose a stubborn design paradigm for nonlinear high-gain observers, resulting in enforcing a saturation nonlinearity with variable limits on the output injection term. We analyze the input-to-state stability properties of the estimation error dynamics, and we show that the stubborn extension does not lead to a worse bound than the original high-gain design in terms of both peaking and sensitivity to disturbances and measurement noise. We illustrate by simulation that the proposed “stubborn” modification is actually effective at improving the transient response of the observer and the rejection of measurement outliers.