Consensus Control of Second-Order Time-Delayed Multiagent Systems in Noisy Environments Using Absolute Velocity and Relative Position Measurements

This article designs an effective consensus control protocol for continuous-time second-order time-delayed multiagent systems in a multiplicative noisy environment, using absolute velocity and relative position measurements. The nonlinear case and double-integrator case are studied, respectively. Due to the time delay and multiplicative noise in such models, the conventional methods for consensus analysis are not applicable. In this article, therefore, a degenerated Lyapunov functional is used to derive the conditions for mean-square consensus and almost-sure consensus, related to the Lipschitz constants of the nonlinear term, time delay, and noise intensity. In particular, for the double-integrator setting, it is shown that the mean-square consensus and the almost-sure consensus can be achieved by choosing appropriate control gains for any given time delay and noise intensity. To show the effectiveness of the proposed control protocol, some numerical simulations are demonstrated.