On the control of the Hegselmann-Krause model with leadership and time delay

Abstract: We analyze Hegselmann-Krause opinion formation models with leadership in presence of time delay effects. In particular, we consider a model with pointwise time variable time delay and a model with a distributed delay. In both cases we show that, when the delays satisfy suitable smallness conditions, then the leader can control the system, leading the group to any prefixed state. Some numerical tests illustrate our analytical results.