Rotating consensus analysis and design for linear multi-agent systems

This paper presents a new method to analyze the rotating consensus problem of linear multi-agent systems (MASs). First, we convert the rotating consensus problem of the original system into a consensus problem of corresponding new system by a model transformation, and also introduce the consensus protocol of the original system to achieve consensus. Then, a proper linear transformation is proposed to transform the consensus problem of the new system into a partial stability problem of corresponding auxiliary system. Meanwhile, we design the gain matrix of the protocol by solving a bilinear matrix inequality via the path-following method. Numerical examples of directed and undirected information topologies are given to illustrate the effectiveness of the theoretical results.