Interval Consensus of Hybrid Multi-Agent Systems Over Cooperative-Antagonistic Network

This paper considers the interval consensus problem for a class of hybrid linear multi-agent systems with periodic jumps over a signed digraph, without assuming specific connectivity properties. By utilizing the concept of independent strongly connected components, we provide a clear characterization of network clusters and explicitly depict the consensus behavior of a trajectory. A hybrid distributed state feedback approach is developed to achieve the convergence of agents under stabilizable condition in the hybrid time domain. Importantly, our results establish the solvability of the interval consensus problem for both discrete-time and sampled-data continuous-time multi-agent systems under signed graphs. To validate the theoretical findings, a practical interval consensus of multiple bouncing disks is studied and simulated.