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

Exact controllability and stability of the Sixth Order Boussinesq equation