01234nas a2200133   4500000000100000000000100001000000100002008004100003100001700044245007200061300001200133490000700145520094800152       2007                            d1 aJerzy Klamka00aStochastic controllability of linear systems with delay in control.  a23–290 v553 aIn the paper finite-dimensional stationary dynamical control systems described by linear stochastic ordinary differential state equations with single point delay in the control are considered. Using notations, theorems and methods taken directly from deterministic controllability problems, necessary and sufficient conditions for different kinds of stochastic relative controllability are formulated and proved. It will be proved that under suitable assumptions relative controllability of a deterministic linear associated dynamical system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamical system. Some remarks and comments on the existing results for stochastic controllability of linear dynamical systems with delays are also presented. Finally, minimum energy control problem for stochastic dynamical system is formulated and solved.