Robust Prescribed-Time Coordination Control of Signed Networks With Arbitrary Topologies

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