Finite-Time and Fixed-Time Bipartite Consensus Tracking of Multi-Agent Systems With Weighted Antagonistic Interactions

This paper is concerned with the problem of bipartite consensus tracking for multi-agent systems with both cooperative and antagonistic interactions. These interactions among vertices in a signed digraph are first investigated with the signs of the weighted products of associated paths in their augmented undirected graph. To improve the convergence rate, a finite-time protocol and a fixed-time protocol are developed to solve the bipartite consensus tracking problem with a finite-time and a settling time independent of any initial states, respectively. Moreover, an M-matrix based method is well proposed to estimate all parameters in the constructed Lyapunov function, therefore, the upper bounds of the settling times for finite-time and fixed-time cases can be analytically determined. Finally, numerical examples are provided to demonstrate the effectiveness of proposed methods.