On controllability of linear systems with time delays in control

The problems of controllability of linear processes with time delays described by the differential equationdot{x}(t) = A(t)x(t) + summin{i=0}max{k} B_{i}(t)u(t-h_{i}and satisfied in Euclidean space Rⁿare considered. The necessary and sufficient conditions for controllability, using the transition matrix of the process, are given. By the additional assumption that the matricesA,B_{i}are analytic int, another criterion of controllability, using the matricesAand Bionly, is proved.