Wave propagation in abstract dynamical system with boundary control

Let $L_0$ be a positive definite operator in a Hilbert space $\mathcal{H}$ with the defect indexes $n_{\pm }⩾1$ and let $\{\mathrm{K}\mathrm{e}\mathrm{r}{L}_0^{\ast };{\mathrm{\Gamma }}_1,{\mathrm{\Gamma }}_2\}$ be its canonical (by M.I.Vishik) boundary triple. The paper deals with an evolutionary dynamical system of the form \begin{align*} & u_{tt}+{L_0^} u=0 &&$\text{in}$,,{\mathscr H},,,,t>0;\ & u\big|{t=0}=u_t\big|{t=0}=0 && {\rm in},,{\mathscr H};\ & Γ_1 u=f(t), && t\geqslant 0, \end{align} where $f$ is a boundary control (a $\mathrm{K}\mathrm{e}\mathrm{r}{L}_0^{\ast }$-valued function of time), $u=u^f(t)$ is a trajectory. Some of the general properties of such systems are considered. An abstract analog of the finiteness principle of wave propagation speed is revealed.