Stationary bipartite consensus of second-order multi-agent systems: an impulsive approach

This paper studies the stationary bipartite consensus problem of a kind of multi-agent systems with second-order dynamics, where the impulsive control approach is utilized to design the control protocol. The impulsive control law is only considered by using position-based information, and the structure of control law is induced by a structurally balanced graph. Then, the stationary bipartite consensus problem has been converted to a convergence problem with respect to a finite product of stochastic matrices. By using the norm matrix and convex theory, this convergence problem is proven to be stability, which means that the stationary bipartite consensus problem is ensured. Subsequently, a numerical example is given to show the obtained result.