Balancing Transformations for Infinite-Dimensional Control Systems

In order to facilitate model reduction by balanced truncation, we introduce state space transformations that can be used to construct an ℓ₂-balanced realization of a regular, linear input-ouput map with nuclear Hankel-operator directly from the system generators of an arbitrary, given realization. These balancing transformations are based on factors of the Gramians and, for infinite-dimensional systems, they are usually unbounded operators. Subsequently the ℓ₂-balanced realization can be truncated in a non-trivial way to obtain an approximating, finite-dimensional model. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

ChemInform Abstract: Instability of the Al42‐ “All‐Metal Aromatic” Ion and Its Implications.

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