Observers for systems with nonlinearities satisfying an incremental quadratic inequality

We consider the problem of designing observers to asymptotically estimate the state of a system whose non-linear time-varying terms satisfy an incremental quadratic inequality that is parameterized by a set of multiplier matrices. Observer design is reduced to solving linear matrix inequalities for the observer gain matrices. The proposed observers guarantee exponential convergence of the state estimation error to zero. In addition to considering a larger class of nonlinearities than previously considered, this paper unifies some earlier results in the literature. The results are illustrated by application to a model of an underwater vehicle.