In this paper, the problem of non-negative edge consensus of undirected networked linear time-invariant systems is addressed by associating each edge of the network with a state variable, for which a distributed algorithm is constructed. Sufficient conditions referring only to the number of edges are derived for non-negative edge consensus of the networked systems. Subsequently, the linear programming method and a low-gain feedback technique are introduced to simplify the design of the feedback gain matrix for achieving the non-negative edge consensus. It is found that the low-gain feedback technique has a good effect on the non-negative edge consensus of the networked systems subject to input saturation. Numerical simulations are presented to verify the effectiveness of the theoretical results.

中文翻译：

---

达成网络动力系统的非负边缘共识


本文通过将网络的每条边与状态变量相关联来解决无向网络线性时不变系统的非负边一致性问题，并为此构建了分布式算法。导出了仅涉及边数的充分条件，以实现网络系统的非负边一致性。随后，引入线性规划方法和低增益反馈技术来简化反馈增益矩阵的设计，以实现非负边沿一致。研究发现，低增益反馈技术对于输入饱和的网络系统的非负边一致具有良好的效果。数值模拟验证了理论结果的有效性。