Fixed-time consensus of nonlinear multi-agent systems with stochastically switching topologies

In this paper, the fixed-time consensus issue of nonlinear multi-agent systems with general time-varying topologies and stochastically switching topologies is investigated. Firstly, for the case of general time-varying topologies, an appropriate nonlinear control protocol is proposed, the sufficient criterion for fixed-time consensus is derived by utilising the method basing on the scramblingness property of the system's weighted adjacency matrix. Then, based on the derived general theorem, the case of stochastically switching topologies is investigated. We mainly focus on the scenarios of (i) independent and identically distributed switching topologies and (ii) Markovian switching topologies. For both scenarios, it is proved that, if the probability of a scrambling weighted adjacency matrix is nonzero, then the fixed-time consensus can be realised almost surely when the involved control parameters are properly selected. Some simulations are presented at last to verify the obtained theorems.