LAUSR

In this article, the couple-group secure consensus of a kind of heterogeneous multi-agent systems (HMASs) with cooperative-competitive relation and time delays has been investigated if it receives malicious attacks. Based on cooperative-competitive relation and time delays, a new couple-group secure consensus protocol is designed. By applying the graph theory, linear algebra theory, probability theory, the linear combination theory and Getschgorin theorem, several sufficient conditions have been obtained to realize the couple-group secure consensus for this system. The obtained results also show the upper limitation of input delay can be computed if the parameters of system are given. It worth pointing out the topology of HMASs is no more needed to contain a spanning tree or meet with the balance of in or out degree in the obtained results. In additional, an adaptive function is added to speed up the convergence of consensus. Combined these obtained results with T-test, a novel detection algorithm has also been designed to determine that the nodes are security or not. Some examples have been given to prove the effectiveness of these obtained results and the improved secure detection algorithm.