Bounded real and positive real balanced truncation for infinite-dimensional systems

Christopher Guiver, Mark R. Opmeer

Research output: Contribution to journalArticle

2 Citations (Scopus)
118 Downloads (Pure)

Abstract

Bounded real balanced truncation for infinite-dimensional systems is considered. This provides reduced order finite-dimensional systems that retain bounded realness. We obtain an error bound analogous to the finite-dimensional case in terms of the bounded real singular values. By using the Cayley transform a gap metric error bound for positive real balanced truncation is subsequently obtained. For a class of systems with an analytic semigroup, we show rapid decay of the bounded real and positive real singular values. Together with the established error bounds, this proves rapid convergence of the bounded real and positive real balanced truncations.
Original languageEnglish
Pages (from-to)83-119
Number of pages36
JournalMathematical Control and Related Fields
Volume3
Issue number1
DOIs
Publication statusPublished - Mar 2013

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