Semi-global nite-time observers for a class of non-Lipschit systems *

In this paper, we extend the semi-global finite-time observers design to a broader class of single-output systems that are uniformly observable and possibly non-Lipschitz. The class of systems are characterized by the non-Lipschitz type of conditions with mixed (greater than 1 or less than 1) and varying rational powers of the increments. They include thus as a proper subset of the class of nonlinear systems that were found to admit global asymptotic observers. Finite-time observers can realize the accurate reconstruction of the states in a finite interval of time. This is achieved with a new local finite-time stability result and a gain updated law which is better fitted to the property of the nonlinearities.