Distributed Averaging Problems Over Directed Signed Networks

Average Consensus Tracking of Weight-Balanced Multi-Agent Systems via Sampled Data

“…Based on Theorem 1, we can solve the average consensus tracking problems of multiagent systems under digraphs no matter whether the digraphs are weight-balanced or not. It significantly improves the results of [25,26], in which the strict condition on weight balance is not needed any more.…”

“…Furthermore, we say a node is globally reachable if it can be reached from any other node in the directed graph. If every node in a directed graph is globally reachable, then the directed graph is said to be strongly connected [26].…”

Bipartite Consensus Problems of Directed Cooperative and Antagonistic Networks with Communication Time‐Varying Delays

“…Remark Based on Ref. [36], the signed‐average consensus of the signed network (1) is given by $$$$ \underset{t\to \infty }{\lim }{x}_i(t)=\underset{t\to \infty }{\lim}\frac{\sigma_i}{n}\sum \limits_{i=1}^n{\sigma}_j{x}_j(0),\kern0.5em \forall i\in {\mathrm{\mathcal{I}}}_n $$$$ where $$$ {x}_j(0) $$$ is the initial state of the agent $$$ {v}_j $$$. In comparison with the (19) and (20), there exists essential difference between (19) and (20).…”