Distributed delay control of multi-agent systems with nonlinear dynamics: Stochastic disturbance

• A novel type of integral distributed delay protocol is proposed to control multi-agent systems.
• Sufficient conditions for the mean square bounded consensus are established.
• Numerical examples of complex nonlinear systems verify the effectiveness of the new protocol.

For multi-agent systems, significantly adding to the complexity of dynamical behaviors are intrinsic nonlinearity and stochastic noises due to environmental uncertainties. This paper deals with the mean square bounded consensus problem of multi-agent systems with intrinsic nonlinear dynamics, where each agent is affected by stochastic noises. Considering the impact of the former behaviors of nonlinear agents, we put forward a novel type of integral distributed delay protocol which is formed as a weighted sum of historical information exchange over all time interval [t−τ,t][t−τ,t]. Compared with the previous work, the protocol expression of this paper is more general and includes many traditional protocols as its special cases. Based on a Lyapunov-based approach, together with results from matrix theory and algebraic graph theory, sufficient conditions are derived for the mean square bounded consensus. Simulation examples with nonlinear even chaotic agents illustrate the theoretical results.