Consensus and performance optimisation of multi-agent systems with position-only information via impulsive control

In this study, the consensus problem of second-order multi-agent systems (MAS) with position-only information is studied. Allowable sampling period for which second-order consensus can be achieved is obtained with two impulsive consensus algorithms. It is shown that if there is at least one eigenvalue of the Laplcian matrix with a non-zero imaginary part, consensus cannot be achieved for sufficiently small or large impulsive periods for both algorithms. Furthermore, the convergence performance of the MAS is optimised. Convergence speed, asymptotical decay factor and per-step decay factor of the error energy are utilised to investigate the convergence performance, and the relationship among impulsive period, topology structure and convergence performance is derived. Finally, numerical examples are given to validate our theoretical results.