Unknown input observer design for a class of nonlinear systems: an LMI approach

A full order nonlinear unknown input observer (NUIO) for a class of Lipschitz nonlinear systems with unknown inputs is designed. A sufficient NUIO existence condition which requires solving a nonlinear matrix inequality is derived. To avoid solving the nonlinear matrix inequality directly, the existence condition is then reformulated as a new sufficient existence condition in terms of an LMI. An important advantage of this LMI based condition is that it enables us to design the proposed full order NUIO using Matlab LMI toolbox and thus makes the difficult NUIO design problem an easy task for the considered class of nonlinear systems. The new sufficient condition, when applied to linear systems, is also necessary. An example is given to show how to use the LMI approach to design the proposed NUIO, and simulation results are presented.