A case study in model reduction of linear time-varying systems

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.