AI 中文总结
本文针对受异质性扰动的多智能体网络系统，研究鲁棒不稳定性半径（RIR），推导其上下界，在网络连接矩阵秩为1等特定条件下可通过小增益论证精确刻画RIR。
AI 中文摘要
本文研究不确定网络系统的鲁棒不稳定性问题。我们考虑由具有相同标称动力学的单输入单输出智能体网络描述的多智能体系统，该系统受异质性扰动影响。网络描述形式化为对角不确定性、标称相同智能体与静态互联矩阵的反馈互联。假设标称网络不稳定，我们寻求鲁棒不稳定性半径（RIR），其定义为使网络稳定的稳定不确定性的最小范数。我们推导了网络稳定性的条件，并得到了RIR的上下界。当网络连接矩阵秩为1且所有对角元素符号相同或为零时，我们给出了通过小增益论证精确刻画RIR的条件。
英文摘要
This paper is concerned with robust instability of uncertain network systems. We consider the multi-agent system described as a network of single-input-single-output agents with identical nominal dynamics subject to heterogeneous perturbations. The network description is formalized as a feedback interconnection of a diagonal uncertainty, nominal identical agents, and a static interconnection matrix. Assuming that the nominal network is unstable, we seek the robust instability radius (RIR), defined as the smallest norm of the stable uncertainty that renders the network stable. Conditions for the network stability are developed, and upper and lower bounds on the RIR are derived. When the network connectivity matrix is rank one and all diagonal entries share the same sign or are zero, we give conditions under which the RIR is exactly characterized by a small gain argument.
