Tracking consensus of nonlinear MASs with asymmetric communication delays in noisy environments

•The tracking consensus analysis method for stochastic MASs is novel.•The asymmetric communication delays is focused on in this paper.•The delays is time-varying, and one derives its upper bound.•This paper also focuses on noise, directed topology, and nonlinear dynamics.

This paper investigates the tracking consensus problem of nonlinear multi-agent systems (MASs) with asymmetric time-varying communication delays in noisy environments under the conditions of fixed and switching directed topologies. A novel stochastic analysis approach is proposed, which guarantees that the designed two distributed tracking protocols can guide the controlled systems to achieve tracking consensus in the sense of mean square. In order to further reveal the influence of asymmetric communication delays on the tracking consensus ability for MASs, some new delay-dependent sufficient conditions for mean-square consensus are also developed. A simple example is finally given to illustrate the effectiveness of the proposed theoretical results.