H ‘ synthesis of unknown input observers for non - linear Lipschitz systems

The problem of unknown input observer design for non-linear Lipschitz 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 dynamic framework are used to deal with the Lipschitz non-linearity. The necessary and sufficient condition that ensures asymptotic convergence of the new observer is presented, and the equivalence between this condition and an H1 optimal control problem which satisfies the standard regularity assumptions in the H1 optimization theory is shown. Based on these results, a design procedure that is solvable using commercially available software is presented. A simulation example is given to illustrate the proposed design.