We consider the problem of designing observers to asymptotically estimate the state of a system whose nonlinear 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 earlier related results in the literature. The results are illustrated by application to several examples. (C) 2011 Elsevier Ltd. All rights reserved.