Prescribed-time bipartite consensus for signed directed networks on time scales

Abstract

This note deals with the prescribed-time consensus problem for multi-agent systems over directed networks with hybrid cooperative and antagonistic interactions on time scales. Different from the regular finite/fixed-time control where the settling time depends on the system initial conditions or the system parameters, the proposed prescribed-time control protocol can directly lead to a predetermined convergence time. Existing results on finite/fixed-time consensus all require the considered network topologies depicted by undirected graphs or strongly connected and detail-balanced directed graphs. In this note, by resorting to a prescribed-time function and the direct Lyapunov method, it is shown that the prescribed-time bipartite consensus can be realised, which only requires the directed network topology to be strongly connected. In addition, based on the theory of time scales, a unified prescribed-time protocol is firstly proposed to solve the consensus problem for both continuous-time and discrete-time multi-agent systems simultaneously.