LAUSR

This paper studies the bipartite consensus issue of networked delayed singularly perturbed systems with antagonistic interactions and switching topologies. Each singularly perturbed system contains both fast and slow dynamics as well as time-varying delay, which make the model a nonstandard singularly perturbed system. The focus is on designing a new distributed protocol such that both the fast and slow subsystems of each agent can achieve the desired pattern. The novelty of the proposed distributed protocol is the ability to balance the relationships between the fast and slow dynamics by introducing the singular perturbation parameter into the protocol. A novel method combining the state transformation method with the vector comparison principle is also proposed. This method can not only avoid the decomposition of the model, but also provide the upper bound of the singular perturbation parameter explicitly. Finally, some simulation examples are given to illustrate the effectiveness of the deduced consensus criteria.