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Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics

Fan, Michael K. H. and Tits, André L. and Doyle, John C. (1991) Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics. IEEE Transactions on Automatic Control, 36 (1). pp. 25-38. ISSN 0018-9286.

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Continuing the development of the structured singular value approach to robust control design, the authors investigate the problem of computing μ in the case of mixed real parametric and complex uncertainty. The problem is shown to be equivalent to a smooth constrained finite-dimensional optimization problem. In view of the fact that the functional to be maximized may have several local extrema, an upper bound on μ whose computation is numerically tractable is established; this leads to a sufficient condition of robust stability and performance. A historical perspective on the development of the μ theory is included.

Item Type:Article
Additional Information:© Copyright 1991 IEEE. Reprinted with permission. Manuscript received August 15, 1988; revised August 2, 1989 and April 7, 1990. Paper recommended by Past Associate Editor, J. D. Cobb. The work of M. K. H. Fan and A. L. Tits was supported in part by the National Science Foundation under the Engineering Research Centers Program NSFD-CDR-88-03012 and by the NSF under Grant DMC-84-51515. The work of J. Doyle was supported by NASA, NSF, ONR, and the AFOSR. The authors wish to thank Dr. E. Zafiriou and Dr. A.K. Packard for numerous discussions, L. Lee and P. Young for pointing out inaccuracies in a preliminary version, and anonymous reviewers for providing valuable comments.
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Deposited On:03 Jan 2007
Last Modified:15 Jan 2015 20:41

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