H2 approximation of multiple input/ output delay systems

Many physical multivariable processes can be sufficiently described as linear models with multiple input/output delays. To simplify the synthesis and analysis of control problem, a reduced-complexity model is often desired. In this paper, an H2 model reduction scheme is introduced for stable linear systems with multiple input/output delays. The reduced model can be a finite dimensional linear model, or a linear model with a time delay. In the latter case the approximation can be improved drastically without increasing the order of the finite dimensional part. The stability is preserved in the approximating models by employing a parametrization of linear stable systems. The optimal parameters can be obtained by solving an optimization problem using a gradient-based method. Two chemical numerical examples are used to show the effectiveness of the proposed scheme.