Distributed Formation Control of Singular Multi-Agent Systems

For multi-agent systems consisting of agents described by the high-order linear singular state-space model, formation control problems are investigated. By using Jordan matrix decomposition technique, a sufficient condition for singular multi-agent systems to achieve the formation given in terms of a group of piecewise continuous vector functions, is obtained and the concept of formation feasibility is introduced. Furthermore, it is shown that the stabilizability of singular agents is a sufficient condition for the existence of formation control protocols, and an approach for the formation control protocol design is presented. Finally, a numerical example is presented to demonstrate the effectiveness of theoretical results.