In this paper, the balanced truncation procedure is applied to time-varying linear systems, both in continuous and in discrete time. The methods are applied to a linear approximation of a diesel exhaust catalyst model. The reduced-order systems are obtained by using certain projections instead of direct balancing. An approximate zero-order-hold discretization of continuous-time systems is described, and a new a priori approximation error bound for balanced truncation in the discrete-time case is obtained. The case study shows that there are several advantages to work in discrete time. It gives simpler implementation with fewer computations. (C) 2005 Elsevier Ltd. All rights reserved.