Distributed containment control of a class of multi-agent systems driven by Brownian motion

In this paper, the containment tracking problem of a class of multi-agent systems with multiple leaders is addressed. The agents in the network are assumed to be of general linear dynamics driven by Brownian motion. A distributed containment protocol is proposed and then by employing Ito’s formula, the stochastic stability of the error dynamics is proven. The sufficient conditions for stability in probability are derived in the form of linear matrix inequalities. It is demonstrated that the states of the followers will asymptotically converge to the stochastic convex hull formed by the leaders’ states. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method.