针对一类二阶离散多智能体系统,在多领导者和固定拓扑情形下, 研究了单时滞和多时滞下的系统可控性,运用增广矩阵、可控矩阵、行列式等方法及定义得出了系统可控的充分条件.结果表明整个系统的可控性不仅与跟从者之间的耦合拓扑关系有关,而且与领导者和跟从者之间的信息传递关系有关. 所得结果通过例子进行了验证.

This paper concerns the controllability of second-order discrete-time multi-agent systems with multiple leaders and time-delays. The issue is discussed under fixed topology. Both a single time-delay and multiple time-delays are addressed. By using augmented matrix, controllability matrix and determinant, sufficient controllability conditions are proposed for the multi-agent system with a single time-delay and multiple time-delays, respectively. The results indicate that the controllability of a discrete-time multi-agent system is affected not only by the coupling information among the followers but also by the total coupling weights from the leaders to the followers. Numerical examples are given to illustrate the theoretical results.