Bipartite Consensus of Nonlinear Discrete-time Multi-agent Systems via Variable Impulsive Control

This paper addresses the bipartite consensus of the nonlinear discrete-time multi-agent systems on network where cooperation and confrontation exist simultaneously. The communication graph has negative weights to represent antagonistic interaction among agents. Two kinds of distributed variable impulsive protocols are designed for case with leader and leaderless. Compared with existing fixed-time impulsive protocols, the action instant of variable impulsive protocol is in a time window and not fixed, which is more suitable for practical application. By employing Lyapunov function approach and comparison system theorem, the results reveal that the bipartite leaderless consensus and bipartite tracking consensus can be achieved. Meanwhile, the rate of bipartite consensus possess the characteristic of exponential, if some conditions are met. Finally, the effectiveness of the consensus analysis is verified by three simulation examples.