Leader-following consensus of a class of stochastic delayed multi-agent systems with partial mixed impulses

In this paper, the exponential leader-following consensus problem is investigated for a class of nonlinear stochastic networked multi-agent systems with partial mixed impulses and unknown time-varying but bounded delays. The main feature of partial mixed impulses is that time-varying impulses are not only composed of synchronizing and desynchronizing impulses simultaneously but they are also injected into a fraction of nodes in multi-agent systems. Three kinds of partial mixed impulses are proposed: fixed partial mixed impulses, periodic partial mixed impulses, and try-once-discard-like partial mixed impulses. By means of the Lyapunov function theory and the comparison principle, conditions are derived for ensuring global exponential leader-following consensus under the presented three kinds of partial mixed impulses. Simulations of leader-following consensus of robotic systems are provided to validate the effectiveness of the proposed results and to show the advantages of the proposed partial mixed impulses.