| Contents |
| Let $V\subset X\subset V^{\prime }$ are Hilbert spaces with continuous dense
injections (see more details in [3] and references therein).
%\cite{Tucsnak&Weiss}
Consider the control evolution equation [1] %\cite{Hille&Philips}
%\begin{equation}
\begin{equation*}
\dot{x}\left( t\right) =Ax\left( t\right) +bu\left( t\right) ,x\left(
0\right) =x^{0},0\leq t0$ there exists a square integrable control $u\left( \cdot
%\right) \in L_{2}(\left[ 0,t_{1}\right],\mathbb{R}^r)$ such that a mild
%solution $x\left( t,x^{0},u\left( \cdot \right) \right) $ of equation (\ref%
%{1}) with initial condition $x^{0}$, generated by a control $u\left( \cdot
%\right) $, satisfies the condition $\left\Vert x\left( t,x^{0},u\left( \cdot
%\right) \right) \right\Vert |
|