Impulsive bipartite consensus of second-order multi-agent systems without relative velocity information

Abstract

In this paper, the bipartite consensus problem is considered for a type of second-order multi-agent system. Using the signed graph theory, the control protocol is designed by means of a distributed impulsive control strategy. Then, the problem is transformed into a convergence problem that is presented by the products of a group of general stochastic matrices, where the general stochastic matrix means that each row sum is equal to 1 and all entries are not required to be nonnegative. To analyze such a convergence problem, some convex hulls are constructed. It is shown that these convex hulls are contractive under the effect of the products of these general stochastic matrices. Subsequently, a sufficient criterion is derived to ensure the impulsive bipartite consensus of the system being considered. Finally, two numerical examples are given to illustrate the result.