In this paper, the controllability problem is addressed for a two-time-scale discrete-time system with multiple agents. First, the system is described by a singularly perturbed difference equation expressed on fast timescale. Then, to eliminate the singular perturbation parameter, by using the iterative method and approximate approach, the two-time-scale system is separated into slow and fast subsystems. Subsequently, some sufficient and/or necessary conditions of controllability for the systems are derived by using matrix theory. Moreover, under three special network topologies, the necessary criteria for controllability are proposed via graph theory. Finally, we give a simulation example to illustrate the effectiveness of the proposed theoretical results.

中文翻译：

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两时间尺度离散时间多智能体系统的可控性


本文解决了具有多个智能体的两时间尺度离散时间系统的可控性问题。首先，系统由快速时间尺度上表达的奇扰动差分方程来描述。然后，为了消除奇异扰动参数，采用迭代法和近似法，将二时间尺度系统分为慢子系统和快子系统。随后，利用矩阵理论推导出系统可控性的一些充分和/或必要条件。此外，在三种特殊的网络拓扑下，通过图论提出了可控性的必要标准。最后，我们给出了一个仿真例子来说明所提出的理论结果的有效性。