Nu-gap model reduction in the frequency domain

In this paper a model reduction algorithm in the nu-gap metric is considered. The metric was originally developed to evaluate robustness of a controller for a given plant. In fact, the nu-gap metric induces the weakest topology in which stability is a robust property. All in all the nu-gap metric is perhaps the best metric to evaluate the distance between two systems in a closed loop setup. In the field of distributed control, if approximation of the subsystems is considered, such a metric can be vital for modeling purposes. The presented algorithm of model reduction in the nu-gap metric is based on semidefinite programming methods and exploits the frequency domain representation of the systems. Therefore it may be easily extended to incorporate into the optimization procedure constraints on a specific frequency region of a particular interest or the closed loop performance.