On an evolutionary dynamical system of the first order with boundary control

The work is carried out as part of a program to construct a new functional (so-called wave) model of symmetric operators. It is shown that an abstract evolutionary dynamic system of the first order (w.r.t. time) with boundary control, which is determined by a symmetric operator $L_0:{\mathscr H}\to{\mathscr H}$, is controllable if and only if $L_0$ has no maximal symmetric parts in ${\mathscr H}$.