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.
Original language | English |
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Pages (from-to) | 1366-1401 |
Number of pages | 36 |
Journal | SIAM Journal on Control and Optimization |
Volume | 52 |
Issue number | 2 |
Early online date | 29 Apr 2014 |
DOIs | |
Publication status | Published - 31 Dec 2014 |
Keywords
- infinite-dimensional system
- model reduction
- Hankel operator
- realization
- balanced realization
- optimal Hankel norm approximation