On Grammian-based reduction methods for moderate size systems

Paper in proceeding, 2012

Over the last decades, there has been a constantly increasing interest in the compact reduced dynamical models. The central idea of model reduction is to systematically capture the main input-output properties by a much simpler model than needed for describing the entire states of the system. Among the most popular model reduction approaches, particularly in systems in the order of a couple of thousands, singular value decomposition based are most common model reduction schemes. In this note, a survey of Grammian-based model reduction techniques for moderate size systems is presented. Comments regarding their properties and discussion about their computational issues are given. Computational efforts needed in reduction methods based on Sylvester and Lyapunov equation are being compared. This investigation is followed by a numerical moderate-size example with dense clusters of close eigenvalues. Finally, results of the competing reduction approaches are compared with respect to computational cost and approximation error for same size approximants.