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

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. (c) 2019 Elsevier B.V. All rights reserved.