Group consensus for a class of heterogeneous multi-agent networks in the competition systems

Abstract

In this paper, we investigate the group consensus issues of a continuous-time heterogeneous multi-agent networks. The system consists of two types of agents, the first-order and second-order, respectively. Be distinct from the related works, we propose a new distributed group consensus protocol which modeled by the agents’ competition interaction. Based on stability theory and the method of frequency domain, the systems’ group consensus including these two cases are discussed: without and with the influence of time delays. Meanwhile, the corresponding criteria are theoretically obtained. Specially, these criteria we obtained do not rely on the conservative conditions which exist in the relevant research works, such as in-degree balance and so on. Furthermore, we also theoretically establish the tolerable upper bounds of the time delays for achieving group consensus. The validity of our findings is verified through some numerical simulation examples.