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This work considers the leader-following problem of a network of agents with nonlinear dynamics. To reflect a more practical case, the network topology is assumed to be arbitrarily switching among a finite set of topologies and the time-varying delay exists in the coupling of agents. Based on the common Lyapunov function theory, sufficient conditions for the asymptotical stability of this multiagent system are derived, which in turns, can be managed by the linear matrix inequality method. A sufficient stability condition is derived to provide a tight condition for stability, applicable for networks with considerable sizes. On the other hand, when a multitude of agents is involved, a comparative conservative but efficient criterion is also proposed. Both criteria only demand on low dimensional matrices, which are independent of the network size. Moreover, some simple stability criteria for the cases without coupling delay are also established. A simple optimization scheme is also formulated to determine the largest allowable delay. Finally, numerical simulations are provided to illustrate the feasibility and effectiveness of the obtained theoretical results.