Mean Square Consensus of Multi-agent Systems with Multiplicative Noises and Time Delays under Directed Fixed Topologies

This paper investigates the mean square consensus problem of multi-agent systems impacted by the combined uncertainty of multiplicative noises and time delays. Considering general network under directed fixed topologies, we propose consensus protocol that take into account both the multiplicative noises and time delays. Using tools from stochastic differential delay equation (SDDE), martingale theory and stochastic inequality, we establish sufficient conditions and obtain the explicit consensus gain and delay upper bounds under which the proposed protocol leads to mean square consensus. In addition, we compare the impact of multiplicative and additive noise and reach the conclusion that multiplicative noises have the property of stabilizing effect. Simulations demonstrate the theoretical results.