Consensus of second order discrete-time multi-agent systems with switching topology

Over the last few years, the second order multi-agent systems (MAS) have been intensively investigated. It is well known that most of known results on the consensus of second order MAS depend on an important assumption that all system matrices have a common left eigenvector. This is because that a common quadratic Lyapunov function can be constructed based on the above assumption. To overcome the nonexistence of a common left eigenvector, a convex analysis approach is introduced in this paper. In particular, several consensus criteria are obtained under the condition of nonexistence of a common left eigenvector. It indicates some potential engineering applications in the near future.