Pinning Control Strategies for Bipartite Consensus in Nonlinear Hybrid Singular Switched Multi-Agent Systems

In this study, we have determined the leader-following bipartite consensus conditions for nonlinear singular switched multi-agent systems on non-uniform time domains, using a signed network topology. We present an innovative algorithm based on time scales to effectively address the challenge of structural balance within the signed network. We achieve bipartite consensus and global asymptotic stability conditions for structurally balanced and unbalanced signed networks, respectively. To address both scenarios, we have designed the controllers by using the pinning control methods. In the end, a simulation-based example is discussed with hybrid time domains to validate the proposed theory.