Guiver, C. and Opmeer, M. R., 2011. A counterexample to "positive realness preserving model reduction with H-infinity norm error bounds". IEEE Transactions on Circuits and Systems. Part I: Regular Papers, 58 (6), pp. 1410-1411.
We provide a counterexample to the H-infinity error bound for the difference of a positive real transfer function and its positive real balanced truncation stated in "Positive realness preserving model reduction with H-infinity norm error bounds," IEEE Trans. Circuits Syst, I, Fundam. Theory Appl., vol. 42, no. 1, pp. 23-29 (1995). The proof of the error bound is based on a lemma from an earlier paper, " A tighter relative-error bound for balanced stochastic truncation," Syst. Control Lett., vol. 14, no. 4, 307-317 (1990), which we also demonstrate is false by our counterexample. The main result of this paper was already known in the literature to be false. We state a correct H-infinity error bound for the difference of a proper positive real transfer function and its positive real balanced truncation and also an error bound in the gap metric.
|Item Type ||Articles|
|Creators||Guiver, C.and Opmeer, M. R.|
|Uncontrolled Keywords||control theory,reduced order systems|
|Departments||Faculty of Science > Mathematical Sciences|
|Publisher Statement||Guiver_IEEETSCI_2011_58_6_1410.pdf: © 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.|
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