A new approach using multiple Lyapunov functions for bipartite consensus of multi-agents over directed switching signed graphs

This paper investigates a new approach for the bipartite (cooperative–competitive) consensus control design for a class of nonlinear agents with Lipschitz dynamics under directed switching topologies. The design technique utilizes multiple Lyapunov functions (MLFs), inequality-based criteria, and average dwell-time (ADT) for switching instances to develop relaxed and less conservative constraints. The results are derived for structurally balanced signed graphs which switch among different configurations with persistent or frequent directed spanning tree (DST), rooted at the leader node. Further, results are also investigated for the dynamic leader agent with non-zero norm-bounded control input. To the best of our knowledge, bipartite consensus of a generic form of Lipschitz nonlinear agents under directed switching topologies has been addressed for the first time. In addition, advanced concepts of MLFs and ADT are used for dealing with switching among signed communication topologies. Numerical simulations to validate the proposed theoretical analysis are provided for different conditions.