Leader-following consensus of nonlinear singular multi-agent systems under signed digraph

This paper investigates the leader-following consensus problem for a singular multi-agent system with nonlinear dynamics and signed digraph topology. Firstly, an algorithm is proposed to address the structural balance problem of the signed network, which is suitable for all types of signed graphs. Secondly, by usingM-matrix theory, the bipartite consensus conditions for the singular nonlinear multi-agent system are established when the topology digraph is structurally balanced. Thirdly, the global asymptotic stability conditions are presented when the signed network is structurally unbalanced. Both the controllers are designed by using pinning control strategies. Finally, numerical examples are given to illustrate the correctness and effectiveness of the proposed methods.