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This work studies the consensus problem of a group of agents with nonlinear dynamics while directional communications between agents with delay are assumed. To reflect the practical situation of having reconnections or disconnections between agents, the communication topology is considered to be switched within a finite set of digraphs. The consensus criterion with exponential convergence is established by the use of linear matrix inequalities and multiple Lyapunov functional theory. It is interesting to point out that consensus is still possible even though some agents are isolated from the others intermittently. These theoretical results are also well illustrated with numerical simulations.