Abstract This article is devoted to the consensus control for switching networks of multiple agents with linear coupling dynamics and subject to external disturbances, which is transformed into an H ∞ control problem by defining an appropriate controlled output. On this basis, a distributed dynamic output feedback protocol is proposed with an undetermined system matrix, and a condition in terms of linear matrix inequalities (LMIs) is derived to ensure consensus of the multi-agent system with a prescribed H ∞ level. Furthermore, system matrix of the protocol is designed by solving two LMIs. A numerical example is included to illustrate the effectiveness of the proposed consensus protocol. Keywords: consensusmulti-agent systems H ∞ controlexternal disturbancesswitching networks Acknowledgements This work is supported by the NSFC (60374001, 60727002, 60774003), the MOE (20030006003), the COSTIND (A2120061303) and the National 973 Program (2005CB321902).