Leaderless exponential bipartite position consensus with multiple time-varying communication delays and switching signed topologies

This paper addresses the problem of leaderless bipartite position consensus for cooperative/antagonistic Multi-Agent Systems sharing information over signed switching topologies and in the presence of multiple communication time-varying delays. To solve the problem, a delayed distributed control strategy, resilient to the unavoidable communication impairments and disruptions, is proposed. The exponential stability of the overall networked systems is proved by leveraging the orthant gauge transformation, matrix theory and Lyapunov-Krasovskii method. Stability conditions are provided as a set of Linear Matrix Inequalities (LMIs) depending on both the maximum admissible time delay and the average switching dwell-time. The effectiveness of the proposed solution in ensuring the exponential bipartite position consensus is confirmed by an exemplary numerical example.