On simple design of a robust finite-time observer

This paper presents a novel observer that estimates the state of a linear system in the observer canonical form in finite time. Due to the specially selected dynamical gain, the proposed observer is easy to tune and, at the same time, it is robust to external perturbations (e.g., state disturbances and measurement noises). The tuning algorithm consists in solving a simple system of linear matrix inequalities with only two adjustable parameters. Theoretical results and a comparison with homogeneous and prescribed-time observers are illustrated by numerical simulation.