Event-triggering Signed-average Consensus Algorithms under Directed Signed Networks

In this paper, we consider a signed-average consensus problem under signed networks in which the interactions between agents depicted by edges with positive and negative weights. In order to decrease communication and computation burden, two dynamic event-triggering procotols have been proposed under the signed network that is depicted by the signed digraph. We prove that signed-average consensus is reached exponentially when the signed digraph is structurally balanced and strongly connected; state stability is reached when the signed digraph is structurally unbalanced and strongly connected; and Zeno behavior is excluded. Besides, when the underlying topology is structurally balanced (structurally unbalanced, respectively), we show that static event-triggering laws, which also achieve signed-average consensus (state stability, respectively), are special cases of the dynamic event-triggering laws. We also conclude that when all agents cooperate with each other, which implies that the underlying signed digraph collapses into an unsigned digraph, our algorithms still work. Finally, numerical examples are given to verify our theoretical results.