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The aim in model order reduction is to approximate an input-output mapdescribed by a large-scale dynamical system with a low-dimensional andcheaper-to-evaluate reduced order model. While high fidelity can be achieved bya variety of methods, only a few of them allow for rigorous error control. Inthis paper, we propose a rigorous error bound for the reduction of linearsystems with balancing-related reduction methods. More specifically, weconsider the simulation over a finite time interval and provide an a posterioriadaption of the standard a priori bound for Balanced Truncation and BalancedSingular Perturbation Approximation in that setting, which improves the errorestimation while still yielding a rigorous bound. Our result is based on anerror splitting induced by a Fourier series approximation of the input and asubsequent refined error analysis. We make use of system-theoretic concepts,such as the notion of signal generator driven systems, steady-states andobservability. Our bound is also applicable in the presence of nonzero initialconditions. Numerical evidence for the sharpness of the bound is given.

A time domain a posteriori error bound for balancing-related model order reduction