Finite-time and fixed-time bipartite consensus of multi-agent systems under a unified discontinuous control protocol

This paper investigates the issue of finite/fixed-time bipartite consensus (FFTBC) of multi-agent systems with signed graphs. A new unified framework of finite-time and fixed-time bipartite consensus is built via some discontinuous control protocols based on the theory of differential inclusion and set-valued Lie derivative. Under the structurally balanced or unbalanced signed graphs, the goal of FFTBC is reached by a common discontinuous controller with different control gains, which fills the gap in studying FFTBC issues with discontinuous protocols. Some numerical examples with comparisons are given to demonstrate the effectiveness of our designs.