Design of a Globally and Exponentially Convergent State Observer and its Application to a Mechanical System with Coulomb Friction

Abstract

We show that there always exists a globally and exponentially convergent state-observer for a class of nonlinear systems with nonlinearities that need not satisfy locally Lipschitz condition. So it can be applied to a mechanical system with discontinuous nonlinearities such as Coulomb friction. We not only provide a rigorous proof of convergence of our proposed observer but also how to systematically design it. Through simulation results, the validity of the proposed observer is verified.