  The article studies the exact controllability and the stability of the sixth
order Boussinesq equation
  \[ u_{tt}-u_{xx}+\beta u_{xxxx}-u_{xxxxxx}+(u^2)_{xx}=f, \quad \beta=\pm1, \]
  on the interval $S:=[0,2\pi]$ with periodic boundary conditions.
  It is shown that the system is locally exactly controllable in the classic
Sobolev space, $H^{s+3}(S)\times H^s(S)$ for $s\geq 0$, for "small" initial and
terminal states. It is also shown that if $f$ is assigned as an internal linear
feedback, the solution of the system is uniformly exponential decay to a
constant state in $H^{s+3}(S)\times H^s(S)$ for $s\geq 0$ with "small" initial
data assumption.
