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Computational complexity of μ calculation

Braatz, Richard P. and Young, Peter M. and Doyle, John C. and Morari, Manfred (1994) Computational complexity of μ calculation. IEEE Transactions on Automatic Control, 39 (5). pp. 1000-1002. ISSN 0018-9286. doi:10.1109/9.284879.

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The structured singular value μ measures the robustness of uncertain systems. Numerous researchers over the last decade have worked on developing efficient methods for computing μ. This paper considers the complexity of calculating μ with general mixed real/complex uncertainty in the framework of combinatorial complexity theory. In particular, it is proved that the μ recognition problem with either pure real or mixed real/complex uncertainty is NP-hard. This strongly suggests that it is futile to pursue exact methods for calculating μ of general systems with pure real or mixed uncertainty for other than small problems.

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Doyle, John C.0000-0002-1828-2486
Additional Information:© 1994 IEEE. Manuscript received July 21, 1992; revised March 25, 1993. The work of R. D. Braatz was supported by the Fannie and John Hertz Foundation. The authors thank Prof. J. Tsitsiklis at Massachusetts Institute of Technology, Cambrdige, for his comments.
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Fannie and John Hertz FoundationUNSPECIFIED
Subject Keywords:computational complexity; stability
Issue or Number:5
Record Number:CaltechAUTHORS:BRAieeetac94
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Official Citation:R. P. Braatz, P. M. Young, J. C. Doyle and M. Morari, "Computational complexity of /spl mu/ calculation," in IEEE Transactions on Automatic Control, vol. 39, no. 5, pp. 1000-1002, May 1994. doi: 10.1109/9.284879
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5370
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Deposited On:15 Oct 2006
Last Modified:08 Nov 2021 20:24

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