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We study a problem of damping a control system described byfunctional-differential equations of natural order $n$ and neutral type withnon-smooth complex coefficients on an arbitrary tree with global delay. Thelatter means that the delay propagates through internal vertices of the tree.Minimization of the energy functional of the system leads to a variationalproblem. We establish its equivalence to a certain self-adjoint boundary valueproblem on the tree for equations of order $2n$ with nonlocal quasi-derivativesand multidirectional shifts of the argument, as well as Kirchhoff-typeconditions emerging at the internal vertices. The unique solvability of bothproblems is proved.

On damping a control system of arbitrary order with global aftereffect on a tree