Structure matters — Some notes on high gain observer design for nonlinear systems

This paper deals with high gain observer design for Lipschitz nonlinear systems. High gain observers are very popular in applications because of their simple implementation with a constant observer gain. In practice, the gain is usually chosen based on eigenvalue placement sufficiently far in the complex left half-plane, where the convergence of the nonlinear observer is verified by simulation. Although this strategy works well in many applications, the exact choice of the observer gain is more complicated. In particular, existing design methods often result in a severe restriction of the maximum allowed Lipschitz constant. In many cases, these bounds on the Lipschitz constant are very conservative. We will show that the maximum admissible Lipschitz constant can be increased significantly if the structure of the system is taken into consideration.