Before revision: Also, we can see that is positive for any (assuming the non-degenerate case where  Ce^{{\boldsymbol {A}t}{\boldsymbol {x}}} B^{Te^{{\boldsymbol {A}}^{T}t}{\boldsymbol {x}}} is not identically zero), and that makes a positive definite matrix.
After revision: Also, we can see that is positive for any (assuming the non-degenerate case where  }t}{\boldsymbol {x}}} e^{{\boldsymbol {A}}^{T}t}{\boldsymbol {x}}} is not identically zero), and that makes a positive definite matrix.