Prescribed-time leader-following group consensus for linear multi-agent systems with delays

This paper challenges the problem of prescribed time group consensus for linear multi-agent systems with delays. By designing the delayed protocols based on prescribed time scaling function, the multi-agent systems can realise group consensus in any preset convergence time, which is independent of both the initial conditions and system parameters. Most existing results on finite or fixed time bipartite consensus, require the considered structurally balanced of strongly connected signed networks. In this paper, prescribed time group consensus, including bipartite consensus as its special item, can be achieved without the assumption of signed balanced networks. In addition, group consensus according to different delays is also presented by resorting the Lyapunov stability and algebraic graph theory. Simulations illustrate the validity and correction of the proposed protocols.