Abstract
This paper investigates the consensus problem for a class of nonlinear second-order multi-agent system with and without external disturbances. First, by making use of some inequality techniques and the designed state feedback controller, a consensus criterion is presented for the multi-agent system. In addition, an adaptive control scheme is also developed to ensure the consensus of the multi-agent system. Moreover, we further discuss the $H_{\infty }$ consensus problem for the multi-agent system, and some $H_{\infty }$ consensus criteria are acquired by using the designed state feedback controller and adaptive state feedback controller. Finally, we propose two numerical examples to verify the effectiveness of these obtained results.
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