Projectional Filtered High‐Gain Observer for a Class of Uncertain Nonlinear Systems Under Noisy Discrete Measurements

ABSTRACT This paper analyzes and designs a novel high‐gain observer for a class of uncertain nonlinear systems under noisy discrete measurements. The studied observer consists of three subsystems. The first element is a projectional high‐gain observer, which ensures that the estimated state belongs to a specified range of values and helps attenuate the peaking phenomenon. The second subsystem is a linear filter that attenuates the output noise. The third component is an output predictor that adapts the observer for nonuniform discrete measurements. The proposed observer is analyzed and designed using a non‐optimal but simple criterion and with the attractive ellipsoid method. Furthermore, the last approach guarantees that the observer gains are optimally tuned by solving a set of linear matrix inequalities. Finally, the performance of the high‐gain observer is highlighted in two numerical examples: The estimation of specific reaction rates and biochemical concentrations of a continuous photobioreactor, and in the robust tracking control of an underwater autonomous vehicle.