Model Reduction based on Mixed H₂ / H_∞ Balanced Realizations

Abstract

This paper presents a mixed H₂ / H_∞ balanced realization and applies this to model reduction. Mixed H₂ / H_∞ balanced realization is a state space description such that solutions of H₂ Lyapunov equation and H_∞ Riccati equation become diagonal matrices simultaneously. It is shown that H_∞ and H₂ norms of any reduced model based on this realization are not greater than those of the original system respectively. Upper bounds of H_∞ norm and H₂ norm of the error system between the original model and the reduced model are also established.