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A linear matrix inequality approach to peak‐to‐peak gain minimization

1996; Wiley; Volume: 6; Issue: 910 Linguagem: Inglês

10.1002/(sici)1099-1239(199611)6

1099-1239

J. Abedor, K. Nagpal, K. Poolla,

Numerical methods for differential equations

International Journal of Robust and Nonlinear ControlVolume 6, Issue 9-10 p. 899-927 Research Article A linear matrix inequality approach to peak-to-peak gain minimization J. Abedor, J. Abedor Ampex Corporation, 401 Broadway, M.S. 3-59, Redwood City, CA 94063, USASearch for more papers by this authorK. Nagpal, K. Nagpal Scientific Systems Inc., 500 W. Cummings Park, Suite 3000, Woburn, MA 01801, USASearch for more papers by this authorK. Poolla, K. Poolla Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USASearch for more papers by this author J. Abedor, J. Abedor Ampex Corporation, 401 Broadway, M.S. 3-59, Redwood City, CA 94063, USASearch for more papers by this authorK. Nagpal, K. Nagpal Scientific Systems Inc., 500 W. Cummings Park, Suite 3000, Woburn, MA 01801, USASearch for more papers by this authorK. Poolla, K. Poolla Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USASearch for more papers by this author First published: November 1996 https://doi.org/10.1002/(SICI)1099-1239(199611)6:9/10 3.0.CO;2-GCitations: 200AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In this paper we take a new approach to the problem of peak-to-peak gain minimization (the L1 or induced L∞ problem). This is done in an effort to circumvent the complexity problems of other approaches. Instead of minimizing the induced L∞ norm, we minimize the * -norm, the best upper bound on the induced L∞ norm obtainable by bounding the reachable set with inescapable ellipsoids. Controller and filter synthesis for * -norm minimization reduces to minimizing a continuous function of a single real variable. This function can be evaluated, in the most complicated case, by solving a Riccati equation followed by an LMI eigenvalue problem. We contend that synthesis is practical now, but a key computational question-is the function to be minimized convex?—remains open. The filters and controllers that result from this approach are at most the same order as the plant, as in the case of LQG and H∞ design. Citing Literature Volume6, Issue9-10November 1996Pages 899-927 RelatedInformation