An algorithm is presented for leader-following synchronization of a multi-agent system composed of linear agents with time delay. The presence of different delays in various agents can cause a synchronization error that does not converge to zero. However, the norm of this error can be bounded and this boundary is presented. The proof of the main results is formulated by means of linear matrix inequalities, and the size of this problem is independent of the number of agents. Results are illustrated through examples, highlighting the fact that the steady error is caused by heterogeneous delays and demonstrating the capability of the proposed algorithm to achieve synchronization up to a certain error.

提出了一种由线性智能体构成的多智能体系统的跟随跟随同步的算法。各种代理中存在不同的延迟会导致同步错误，该错误不会收敛到零。但是，可以限制此错误的范数，并给出此边界。主要结果的证明是通过线性矩阵不等式来表示的，并且此问题的大小与代理数量无关。通过示例对结果进行了说明，强调了稳定误差是由异构延迟引起的事实，并证明了所提出算法的能力，可以实现直至一定误差的同步。