Frequency dependent model phase reduction using convex optimization

Model reduction is a long-standing problem. As model reduction as a frequency domain optimization problem can be conjectured NP-hard, several suboptimal but efficient reduction methods were proposed. The obtained suboptimal reduced model are sometimes far away from the optimal reduced model. In this paper, we propose phase model reduction for obtaining reduced models of stable and strictly minimum phase models, possibly close to optimal model. An efficient solution is presented as a finite dimensional convex optimization problem involving linear matrix inequalities. The motivation for phase model reduction is the practical importance of a good phase approximation. Furthermore, our approach allows to constrain a good approximation on a priori specified frequency intervals, without the introduction of weighting functions. The strong interest of this approach for the model reduction with respect to existing model reduction methods is illustrated by two examples.