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Computation of µ with real and complex uncertainties

Young, Peter M. and Doyle, John C. (1990) Computation of µ with real and complex uncertainties. In: 29th IEEE Conference on Decision and Control. Vol.3. IEEE , Piscataway, NJ, pp. 1230-1235.

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The robustness analysis of system performance is one of the key issues in control theory, and one approach is to reduce this problem to that of computing the structured singular value, mu . When real parametric uncertainty is included, then mu must be computed with respect to a block structure containing both real and complex uncertainties. It is shown that mu is equivalent to a real eigenvalue maximization problem, and a power algorithm is developed to solve this problem. The algorithm has the property that mu is (almost) always an equilibrium point of the algorithm, and that whenever the algorithm converges a lower bound for mu results. This scheme has been found to have fairly good convergence properties. Each iteration of the scheme is very cheap, requiring only such operations as matrix-vector multiplications and vector inner products, and the method is sufficiently general to handle arbitrary numbers of repeated real scalars, repeated complex scalars, and full complex blocks.

Item Type:Book Section
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Doyle, John C.0000-0002-1828-2486
Additional Information:© 1990 IEEE. We would like to thank Andy Packard for helpful discussions, Michael Fan for the use of some preliminary upper bound software, and NSF, ONR, NASA, and Rockwell for financial support.
Funding AgencyGrant Number
Office of Naval Research (ONR)UNSPECIFIED
Rockwell InternationalUNSPECIFIED
Record Number:CaltechAUTHORS:20190313-112035048
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Official Citation:P. M. Young and J. C. Doyle, "Computation of mu with real and complex uncertainties," 29th IEEE Conference on Decision and Control, Honolulu, HI, USA, 1990, pp. 1230-1235 vol.3. doi: 10.1109/CDC.1990.203804
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:93773
Deposited By: Tony Diaz
Deposited On:13 Mar 2019 18:28
Last Modified:16 Nov 2021 17:00

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