On frequency-weighted coprime factorization based controller reduction

We consider the efficient solution of a class of coprime factorization based controller approximation problems by using frequency-weighted balancing related model reduction approaches. It is shown that for some special stability enforcing frequency-weights, the computation of the frequency-weighted controllability and observability grammians can be done by solving reduced order Lyapunov equations. The new approach can be used in conjunction with accuracy enhancing square-root and balancing-free techniques developed for the balancing related coprime factors based model reduction.