Model reduction with time delay

The paper presents a procedure for approximation of a high-order system with rational transfer function by a low-order system with rational transfer function together with a pure time delay. The procedure introduces a delay into the system output and computes the low-order transfer function using truncation of a certain balanced realisation. Error bounds are obtained for both continuous-time and discrete-time cases and one part of the error bound is independent of the reduced-order rational transfer function so that it can be evaluated in advance, thereby aiding the selection of suitable delays. Some examples are presented to illustrate the method, which can be applied to multivariable as well as scalar plants.