The paper addresses a problem of design of distributed robust filters using the recent vector dissipativity theory. The main result is a sufficient condition which guarantees a suboptimal H-infinity level of disagreement of estimates in a network of filters. It involves solving a convex optimization/feasibility problem subject to LMI constraints. The special case of balanced interconnection graphs is also considered. A gradient descent type algorithm is presented which allows the nodes to compute their estimator parameters in a decentralized manner. The proposed approach is applied to the problem of observer-based robust synchronization of a nonlinear network to an isolated node. (C) 2010 Elsevier Ltd. All rights reserved.