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.
Highlights
Approximation of a transfer function by truncation of a balanced state-space realization was first suggested for rational functions by Moore in [21]
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
In the above inequality σk are the distinct singular values of the Hankel operator associated with G, of which there are N and n is the number kept in the reduced order system obtained by balanced truncation Gn
Summary
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