Skip to main content

Research Repository

Advanced Search

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

Guiver, Christopher; Opmeer, Mark R.

Authors

Mark R. Opmeer



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.

Citation

Guiver, C., & Opmeer, M. R. (2013). Bounded real and positive real balanced truncation for infinite-dimensional systems. Mathematical Control and Related Fields, 3(1), 83-119. https://doi.org/10.3934/mcrf.2013.3.83

Journal Article Type Article
Publication Date 2013-03
Deposit Date Jul 23, 2020
Publicly Available Date Aug 13, 2020
Journal Mathematical Control and Related Fields
Print ISSN 2156-8472
Publisher American Institute of Mathematical Sciences
Peer Reviewed Peer Reviewed
Volume 3
Issue 1
Pages 83-119
DOI https://doi.org/10.3934/mcrf.2013.3.83
Keywords positive real., well-posed linear system, Model reduction, infinite-dimensional system, balanced truncation, bounded real
Public URL http://researchrepository.napier.ac.uk/Output/2677379

Files

Bounded Real And Positive Real Balanced Truncation For Infinite-dimensional Systems (accepted version) (531 Kb)
PDF





You might also like



Downloadable Citations