Model reduction by balanced truncation for systems with nuclear Hankel operators

Guiver, Chris; Opmeer, Mark R.

Abstract

We prove the H-infinity error bounds for Lyapunov balanced truncation and for optimal Hankel norm approximation under the assumption that the Hankel operator is nuclear. This is an improvement of the result from Glover, Curtain, and Partington [SIAM J. Control Optim., 26(1998), pp. 863-898], where additional assumptions were made. The proof is based on convergence of the Schmidt pairs of the Hankel operator in a Sobolev space. We also give an application of this convergence theory to a numerical algorithm for model reduction by balanced truncation.

Citation

Guiver, C., & Opmeer, M. R. (2014). Model reduction by balanced truncation for systems with nuclear Hankel operators. SIAM Journal on Control and Optimization, 52(2), 1366-1401. https://doi.org/10.1137/110846981

• Journal Article Type: Article
• Acceptance Date: Feb 25, 2014
• Publication Date: 2014-03
• Deposit Date: Jul 23, 2020
• Publicly Available Date: Aug 11, 2020
• Journal: SIAM Journal on Control and Optimization
• Print ISSN: 0363-0129
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 52
• Issue: 2
• Pages: 1366-1401
• DOI: https://doi.org/10.1137/110846981
• Keywords: infinite-dimensional system, model reduction, Hankel operator, realization, balanced realization, optimal Hankel norm approximation
• Public URL: http://researchrepository.napier.ac.uk/Output/2677358