Design of unknown input observers for Lipschitz nonlinear systems

The problem of unknown input observer design for Lipschitz nonlinear systems is considered. A new dynamic framework which is a generalization of previously used linear unknown input observers is introduced. The additional degrees of freedom offered by this framework are used to deal with the Lipschitz nonlinearity. The necessary and sufficient condition that ensures asymptotic convergence of the new observer is presented, and the equivalence between this condition and an H_∞ optimal control problem which satisfies the standard regularity assumptions in the H_∞ optimization theory is shown. Based on these results, a design procedure that is solvable using commercially available software is presented.