  In this article we investigate model order reduction of large-scale systems
using time-limited balanced truncation, which restricts the well known balanced
truncation framework to prescribed finite time intervals. The main emphasis is
on the efficient numerical realization of this model reduction approach in case
of large system dimensions. We discuss numerical methods to deal with the
resulting matrix exponential functions and Lyapunov equations which are solved
for low-rank approximations. Our main tool for this purpose are rational Krylov
subspace methods. We also discuss the eigenvalue decay and numerical rank of
the solutions of the Lyapunov equations. These results, and also numerical
experiments, will show that depending on the final time horizon, the numerical
rank of the Lyapunov solutions in time-limited balanced truncation can be
smaller compared to standard balanced truncation. In numerical experiments we
test the approaches for computing low-rank factors of the involved Lyapunov
solutions and illustrate that time-limited balanced truncation can generate
reduced order models having a higher accuracy in the considered time region.
