Design of globally asymptotically stable nonlinear observers using Lyapunov functions

We present a method for the design of nonlinear observers using Lyapunov functions. We assume the system is in observable normal form already known from the literature. Based on this normal form the observer design is carried out. In related work some assumptions regarding the nonlinearities are usually made, e.g., Lipschitzness or global boundedness. We show that a very weak growth condition, namely, monotone decreasing behaviour with respect to some variables will enable us to construct globally asymptotically stable observers using an appropriate Lyapunov function. An example which illustrates the power of these new design conditions concludes the paper