Observers for a non-Lipschitz triangular form

We address the problem of designing an observer for triangular non locally Lipschitz dynamical systems. We show the convergence with an arbitrary small error of the classical high gain observer in presence of nonlinearities verifying some Hölder-like condition. Also, for the case when this Hölder condition is not verified, we propose a novel cascaded high gain observer. Under slightly more restrictive assumptions, we prove the convergence of a homogeneous observer and of its cascaded version with the help of an explicit Lyapunov function.