This paper presents a consensus-based robust cooperative control framework for a wide class of linear time-invariant (LTI) systems, namely Negative-Imaginary (NI) systems. Output feedback, dynamic, Strictly Negative-Imaginary (SNI) controllers are applied in positive feedback to heterogeneous multi-input multi-output (MIMO) plants through the network topology to achieve robust output feedback consensus. Robustness to external disturbances and model uncertainty is guaranteed via NI system theory. Cooperative tracking control of networked NI systems is presented as a corollary of the derived results by adapting the proposed consensus algorithm. Numerical examples are also given to demonstrate the effectiveness of proposed robust cooperative control framework. (C) 2015 Elsevier Ltd. All rights reserved.