  When solving partial differential equations numerically, usually a high order
spatial discretization is needed. Model order reduction (MOR) techniques are
often used to reduce the order of spatially-discretized systems and hence
reduce computational complexity. A particular MOR technique to obtain a reduced
order model (ROM) is balanced truncation (BT). However, if one aims at finding
a good ROM on a certain finite time interval only, time-limited BT (TLBT) can
be a more accurate alternative. So far, no error bound on TLBT has been proved.
In this paper, we close this gap in the theory by providing an $\mathcal H_2$
error bound for TLBT with two different representations. The performance of the
error bound is then shown in several numerical experiments.
