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：

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达到网络动力系统的非负边缘共识

本文通过将网络的每个边缘与状态变量相关联，解决了无向网络线性时不变系统的非负边缘一致性问题，为此构造了分布式算法。对于网络系统的非负边缘一致性，得出仅涉及边缘数量的充分条件。随后，引入线性规划方法和低增益反馈技术以简化用于实现非负边缘一致性的反馈增益矩阵的设计。发现低增益反馈技术对遭受输入饱和的网络系统的非负边缘共识具有良好的影响。进行了数值模拟，以验证理论结果的有效性。