  In this paper we establish the interpolatory model reduction framework for
optimal approximation of MIMO dynamical systems with respect to the
$\mathcal{H}_2$ norm over a finite-time horizon, denoted as the
$\mathcal{H}_2(t_f)$ norm. Using the underlying inner product space, we derive
the interpolatory first-order necessary optimality conditions for approximation
in the $\mathcal{H}_2(t_f)$ norm. Then, we develop an algorithm, which yields a
locally optimal reduced model that satisfies the established
interpolation-based optimality conditions. We test the algorithm on various
numerical examples to illustrate its performance.
