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This paper addresses a leader-following consensus problem of a multiagent system with switching jointly reachable interconnection and noncoupling time delays. This problem arises naturally in real multiagent systems such as distributed sensing and collective motion. Neighbor-based rules are designed to realize controlling strategies for these agents described by double integrators. Although the interagent connection structures vary over time and the leader of related graphs may not be globally reachable, a sufficient condition to make all the agents follow the leader is given under a state-feedback switching signal, which is based on an appropriate partition of the state space. The consensus error is estimated in an even noisy environment. Finally, a simulation example is presented to verify the analytical results.