This paper considers the consensus of the leaderfollowing systems with a discrete-time model. The velocity of the active leader is unknown in real time. This paper designs the control laws and observers based on the neighbors to solve the consensus problem. The Lyapunov approach has played an important role in the leader-following systems. It is shown that all agents asymptotically move with the same velocity and position. Moreover, it is also proved that each follower can track the active leader in a noisy-free environment, and the tracking error is estimated in a noisy environment.

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