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This paper addresses the problem of robust fault estimation for multi-agent systems (MASs) under communication constraints. Taking into account the possible data packet loss (DPL) in the information interaction of each subsystem, MASs are remodelled as switching systems by introducing a variable sampling strategy. Then, using the local information among agents, a novel intermediate observer design method based on switching scheme is proposed to estimate faults of MASs. Combining Lyapunov’s criterion and linear matrix inequality, sufficient conditions for the intermediate observer to be exponentially stable and have H∞ performance against bounded disturbances and the DPL are given. Finally, some simulations are provided to verify the effectiveness of the proposed method.