  A model order reduction algorithm is presented that generates a reduced-order
model of the original high-order model, which ensures high-fidelity within the
desired time interval. The reduced model satisfies a subset of the first-order
optimality conditions for time-limited H$_2$-model reduction problem. The
algorithm uses a computationally efficient Krylov subspace-based framework to
generate the reduced model, and it is applicable to large-scale systems. The
reduced-order model is parameterized to enforce a subset of the first-order
optimality conditions in an iteration-free way. We also propose an adaptive
framework of the algorithm, which ensures a monotonic decay in error
irrespective of the choice of interpolation points and tangential directions.
The efficacy of the algorithm is validated on benchmark model reduction
problems.
