CONTROLLABILITY FOR DISTRIBUTED PARAMETER SYSTEMS WITH DELAYS IN CONTROL.

The controllability of distributed parameter systems has recently been explored extensively by several authors along the theory of controllability of dynamical systems with delays. In this paper, these two directions, have been combined and necessary and sufficient conditions derived for relative and absolute approximate controllability. These conditions are obtained by using the general methods for controllability of dynamical systems defined in Banach spaces. Some corollaries, concerning the special cases are presented. The results can be extended to the case of boundary controllability and to systems defined on the ball in Euclidean n-dimensional space.