The role of the condition number and the relative gain array in robustness analysis
dc.contributor.author | Chen, Jie | en_US |
dc.contributor.author | Freudenberg, James S. | en_US |
dc.contributor.author | Nett, Carl N. | en_US |
dc.date.accessioned | 2006-04-10T18:08:14Z | |
dc.date.available | 2006-04-10T18:08:14Z | |
dc.date.issued | 1994-06 | en_US |
dc.identifier.citation | Chen, Jie, Freudenberg, James S., Nett, Carl N. (1994/06)."The role of the condition number and the relative gain array in robustness analysis." Automatica 30(6): 1029-1035. <http://hdl.handle.net/2027.42/31565> | en_US |
dc.identifier.uri | http://www.sciencedirect.com/science/article/B6V21-47X1763-66/2/53ceeed7ae9c777cf9f0a481c7edb078 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/31565 | |
dc.description.abstract | This paper studies deviations of open-loop properties in the presence of modeling uncertainties. Our aim is to gain insights into how open-loop properties and thus potentially closed-loop properties may vary in the face of a diagonally structured uncertainty. We give several estimates for the worst case deviations of the open-loop transfer function in terms of certain structured singular values and their bounds, and also in terms of certain scaled plant condition numbers, the relative gain array, and the block relative gains. Our analysis shows that the estimates in terms of the structured singular values and bounds are tight in general, so are those in terms of the condition numbers for certain cases studied previously in the literature. We show that the worst case deviation will be large when the estimates stated in terms of the structured singular values, or under certain circumstances in terms of the condition numbers, are large. On the other hand, an example is constructed to show that the relative gain array and block relative gains may be optimistic measures in assessing these deviations. The developments here support and reinforce previous conjectures and results which assert that plants with large condition numbers and/or relative gains are potentially difficult to control. | en_US |
dc.format.extent | 683059 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Elsevier | en_US |
dc.title | The role of the condition number and the relative gain array in robustness analysis | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Mechanical Engineering | en_US |
dc.subject.hlbsecondlevel | Industrial and Operations Engineering | en_US |
dc.subject.hlbtoplevel | Engineering | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | The Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, MI 48109, U.S.A. | en_US |
dc.contributor.affiliationother | College of Engineering, University of California, Riverside, CA 92521, U.S.A. | en_US |
dc.contributor.affiliationother | United Technology Research Center, 411 Silver Lane, East Hartford, CT 06108, U.S.A. | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/31565/1/0000492.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1016/0005-1098(94)90197-X | en_US |
dc.identifier.source | Automatica | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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