Conclusion

The approximation of linear models is considered by some to be a closed subject, and while the fundamentals of the techniques developed are unlikely to change much in the future, considerable effort is still required to overcome the numerical problems that can arise in this simple case. In particular, the calculation of error norms remains very delicate when models with tens of thousands of states are involved, and some algorithms remain numerically very sensitive when used on ill-conditioned models.

Moreover, accessible and reliable indicators for analyzing the quality of a reduced model remain largely underdeveloped, particularly for judging the suitability of a reduced model for certain specific tasks such as controller synthesis. Indeed, the techniques presented in this article aim to reproduce the open-loop behavior of a model, but few guarantees exist to prejudge...