  This article targets at addressing the robust prescribed-time coordination
control (PTCC) problems for single-integrator cooperative-antagonistic networks
(CANs) with external disturbances under arbitrary fixed signed digraphs without
any structural constraints. Toward this end, the PTCC problems for nominal
single-integrator CANs without disturbances are first investigated and a fully
distributed control protocol with a time-varying gain, which grows to infinity
as the time approaches the settling time, is proposed utilizing the relative
states of neighboring agents. Then, based on the proposed control protocol for
the nominal single-integrator CANs, a new second-order prescribed-time sliding
mode control protocol is constructed to achieve accurate PTCC for
single-integrator CANs in the presence of external disturbances. Using Lyapunov
based analysis, sufficient conditions to guarantee the prescribed-time
stability, bipartite consensus, interval bipartite consensus, and bipartite
containment of single-integrator CANs without or with disturbances are,
respectively, derived. In the end, numerical simulations are given to confirm
the derived results.
