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Published May 1994 | Published
Journal Article Open

Computational complexity of μ calculation


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.

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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