On actuators number in distributed systems

The aim of this brief paper is to give original results regarding inputs for abstract distributed parameter systems. More precisely we show that if we increase the number of actuators exciting a system, the transfer cost functional will be cheaper. Until now this intuitive result has only been noticed in numerical simulations and for certain classes of distributed parameter systems. The principle of the approach consists to introduce the notion of extended actuators. The results are given for various cases where the actuators can be internal, pointwise or boundary.