Consensus problems for high-dimensional multi-agent systems

As a new area of research, consensus problems for multi-agent systems have been studied extensively in the literature. It is usually assumed that all agents share a common one-dimensional state space. The authors of this study concentrate on the consensus problems of multi-agent systems in the framework of high-dimensional state space. As a basis for the analysis, a general model is first introduced by presenting two typical examples along with some necessary and sufficient conditions for the system to solve a consensus problem. Then the structures of consensus functions are investigated and some algebraic characterisations are given. Finally, a class of switched multi-agent systems are discussed and some sufficient conditions for the possession of the consensus property are provided. Several examples to illustrate the effectiveness of theoretical results are given.