Impulsive consensus of multi-agent systems with only sampled-position information

In this paper, the consensus problem for second-order multi-agent systems with only sampled-position information is studied. Two impulsive consensus algorithms are applied and allowable sampling period for achieving second-order consensus are obtained. It is shown that consensus can not be achieved for a sufficient small or sufficient large sampling period as long as at least one eigenvalue of the Laplacian matrix with nonzero imaginary part for both algorithms. Furthermore, the convergence performance optimization problem is characterized. Asymptotical and per-step decay factors of the error energy are utilized to measure the convergence performance and the relationship among topology structure, sampling period and convergence performance is derived. Finally, two numerical examples are given to demonstrate the effectiveness of our theoretical results.