This paper addresses the problem of distributed leader-following consensus for a multi-agent system with an affine nonlinear term. The communication topology we adopt is an undirected connected graph and the leader sends its information to one or more followers. To make each follower asymptotically synchronize with the leader, a nonlinear distributed control protocol is proposed. Using a Lyapunov function and a matrix theory, we establish sufficient conditions which ensure the consensus of these nonlinear multi-agent systems.Finally, a numerical simulation is provided to verify the effectiveness and usefulness of the developed method.Inspired by natural biological consensus behaviors, considerable attention has been extensively paid to the consensus of agents by virtue of its widespread range of applications in many areas, such as robots, sensor networks, biological systems, formation and cooperative control, just to name a few [1][2][3][4][5][6]. As the most essential and important problems, consensus problems for multi-agent systems have drawn attention greatly in recent years [7][8][9][10]. From first-order systems [7], linear systems [8] to high-order systems [9], and then, nonlinear systems [10], the researches on consensus control are getting deeper. The consensus is considered to be achieved if each agent in the network converges to a certain common value. A principal problem for the consensus control is to construct effective control algorithms and laws based on the neighbor information to make some agents reach consensus under the corresponding topology.In general, the existing results about consensus control concentrate on two types of control problems, namely leaderless consensus and leader-following consensus. The former requests that each agent converges to a certain agreement state [11][12][13], which is related to the initial conditions. For example, the consensus problems for a network of first-order agents are addressed in [11]. Each agent eventually converges to the average of the initial states under balanced digraphs. Recently, consensus of multi-agent systems with a leader has been extensively studied [14][15][16][17], whose goal is to guarantee that a group of agents can track the state trajectory of a leader. In [14], the authors concern the consensus for first-order networks with a time-varying leader. The study in [15] is an extension of [14] from first-order to high-order systems. In [16], the semi-global leader-following consensus is investigated for linear systems, whose actuators are imperfect. In [17], global leader-following consensus is discussed under bounded controls. It is true that with the help of a leader, the application range is enlarged for multi-agent systems.Till now, many results on simple linear multi-agent systems can be found in the open literature, including most references mentioned above. However, in practice, most of engineering problems involve complex nonlinear systems so that results for linear systems do not apply. Hence, the nonlinearities in dynamics have b...
