A numerical method to minimize resource consumption by linear systems with constant delay

A numerical method to minimize the resource consumption by the linear systems with constant time delay in the system phase states was proposed. Its global convergence to the $\varepsilon$-optimal solution was proved. By the $\varepsilon$-optimal solution is meant the feasible control $u(t)$, $t\in[0,T]$, driving the system to the $\varepsilon$-neighborhood of the origin and providing a value of the functional that differs from the optimal one at most by $\varepsilon$.