Robust compound observers design for Lipschitz non-linear systems with unknown input disturbance

Abstract

In this paper, we present a new concept of the robust compound observer for Lipschitz non-linear system with unknown input disturbance, which can simultaneously estimate the system states and unknown input disturbances. The robust compound observer is designed by using the structure principle of the general unknown input observer and the conditions for the existence of the robust compound observer are established. Combined with LMI methods, the designing freedoms are released and LMI existence condition and some verification are given for the compound observers which can asymptotically estimate the system state and unknown input disturbance to any desired accuracy. The presented robust compound observer matrices are calculated using MATLAB LMI toolbox to make the difficult non-linear observer design problem an easy task. Numerical simulation results are presented to validate the approach and the robustness to the system non-linearity and uncertainty.