Generalization of optimal Hankel-norm and balanced model reduction by bilinear mapping

Abstract

In this paper the standard optimal Hankel-norm model reduction and balanced model reduction are generalized to optimal Hankel-norm model reduction and balanced model reduction over a disc in the complex plane. Important properties of the new model-reduction concept such as the monotone property of the generalized Hankel norm with respect to the domain, and the L _∞ error bound over a disc D are given. Applications like the approximation of unstable systems and model reduction for specific working signals are discussed.