Design of a robust nonlinear observer for the nonlinear Lipschitz uncertain systems

A robust nonlinear observer for the Lispschitz nonlinear system with unknown input is addressed and designed. The sufficient existence conditions for asymptotic estimation convergence, which requires solving the nonlinear matrix inequalities, are derived and proved. Using by LMI approach, the existence conditions are then reformulated as the new sufficient existence conditions in the terms of an LMI. The advantage of these conditions based on LMI is that it enables us to design the presented the robust nonlinear observer using Matlab LMI toolbox and makes the difficult nonlinear observer design problem an easy task. A numerical example is included for illustration. The simulation results are presented to validate the approach and enhance the robustness for the system nonlinearity and uncertainty.