Time-varying formation control of linear multiagent systems with time delays and multiplicative noises

This article investigates time-varying formation control problems of linear multiagent systems with time delays and multiplicative noises under the undirected interactive topology. First, the time-varying formation control problem under time delays and multiplicative noises is transformed into the asymptotic stability problem of a closed-loop stochastic system. Then, sufficient conditions for formation feasibility under the unstable and stable formation centers are provided by constructing the Lyapunov functional and the Lyapunov function, respectively. For the case of an unstable formation center, we give the formation feasibility conditions and the explicit formation control design. For the case of a stable formation center, it is proved that the formation can be achieved for any given time delay and noise intensity. Finally, numerical simulations on a group of unmanned aerial vehicles are provided to illustrate the effectiveness of the theoretical results.