Stability of MIMO system by system matrix eigenvalues

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I have a MIMO LTI system described by
$\begin{cases}\mathbf{\dot{x}=Ax+Bu}\\ \mathbf{y=Cx} \end{cases}$
If it is controllable, can I conclude system's BIBO stability provided that all eigenvalues of $\mathbf{A}$ are left half-plane located?
I know it is true for SISO systems, however, I could not find any reference that clearly asserts such a theorem for MIMO systems. Thanks.