Exponential bipartite consensus of fractional‐order non‐linear multi‐agent systems in switching directed signed networks

Abstract

This study considers the exponential bipartite consensus problem of a class of non-linear fractional-order multi-agent systems (FOMASs) in a general coopetition network with signed directed graph, where the signed directed graph is composed of both positive and negative interaction links. Without the assumption of the signed directed graph among agents is fixed and strongly connected, the exponential bipartite consensus problem of non-linear FOMASs is solved by utilising some techniques and tools from signed graph theory, matrix transformation and linear matrix inequalities. For the FOMASs in a fixed signed directed topology containing a spanning tree, the authors design a continuous distributed control protocol which can ensure the bipartite consensus error converges to zero exponentially if the parameters of the protocol are suitably selected. For the FOMASs in directed signed networks with switching topologies only frequently but not always contain a spanning tree, a distributed intermittent control protocol is further designed, where the bipartite consensus error converges to zero exponentially. Numerical simulations are given to show the effectiveness of the designed method.