Generalized Super-Twisting Observer for nonlinear systems

In this paper it is proposed a novel Lyapunov based design of a generalized Super-Twisting Observer for a class of 2-dimensional nonlinear system. The observer can deal with systems whose states are composed of bounded nonlineaer functions.This is the main difference with the classical Super-Twisting observer, in which the second state is only the derivative of the first state. Working with a Strong Lyapunov Function it can be shown sufficient conditions to properly choose the observer gains to ensure finite time convergence to the real states. The observer is tested in a mathematical model regarding to the reduced Glucose-Insulin process. The numerical results have shown a better performance of the observer with lineal compensators in comparison to the classical Super-Twisting Observer. The gains for the observer are designed in order to compensate a more general class of perturbations that appear in the suggested glucose-insuline nonlinear model.