In this paper, second-order multi-agent systems with intentionally induced delay are studied, which cannot achieve consensus with a non-delay position-based protocol. Under the proposed distributed protocol with the current and outdated position states, the crossing frequencies and crossing delays of the related quasipolynomial of the delayed systems are identified. By determining the crossing directions of the imaginary roots, the change of the number of the right half-plane roots can be obtained. Accordingly, consensus condition and consensus delay range are provided. Simulations illustrate the effectiveness of the theoretical analysis.

中文翻译：

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故意延迟有利于二阶多智能体系统的共识

在本文中，研究了具有故意诱导延迟的二阶多智能体系统，该系统无法与非延迟基于位置的协议达成共识。在具有当前和过时位置状态的拟议分布式协议下，识别延迟系统的相关拟多项式的交叉频率和交叉延迟。通过确定虚根的交叉方向，可以得到右半平面根个数的变化。因此，提供了共识条件和共识延迟范围。仿真说明了理论分析的有效性。