Impulsive consensus algorithms for second-order multi-agent networks with sampled information

In this paper, the distributed consensus problem for second-order continuous-time multi-agent networks with sampled-data communication is investigated. Motivated by impulsive control strategy, two kinds of impulsive distributed consensus algorithm are proposed. These algorithms only utilize the sampled information and are implemented at sampled times. By using the stability theory of impulsive systems and properties of the Laplacian matrix, necessary and sufficient conditions are obtained to ensure the consensus of the controlled networks. It is shown that the control gains, the sampling period and the eigenvalues of the Laplacian matrix of the communication graph play key roles in achieving the consensus. A numerical example is given to illustrate the results.