Computational complexity of /spl mu/ calculation

The structured singular value /spl mu/ measures the robustness of uncertain systems. Numerous researchers over the last decade have worked on developing efficient methods for computing /spl mu/. This paper considers the complexity of calculating /spl mu/ with general mixed real/complex uncertainty i...

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Bibliographic Details
Published in:IEEE transactions on automatic control 1994-05, Vol.39 (5), p.1000-1002
Main Authors: Braatz, R.P., Young, P.M., Doyle, J.C., Morari, M.
Format: Article
Language:English
Subjects:
Argon
Artificial intelligence
Computational complexity
Constraint theory
Gold
Linear programming
Polynomials
Quadratic programming
Robustness
Uncertainty
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Summary:The structured singular value /spl mu/ measures the robustness of uncertain systems. Numerous researchers over the last decade have worked on developing efficient methods for computing /spl mu/. This paper considers the complexity of calculating /spl mu/ with general mixed real/complex uncertainty in the framework of combinatorial complexity theory. In particular, it is proved that the /spl mu/ 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 /spl mu/ of general systems with pure real or mixed uncertainty for other than small problems.< >
ISSN:0018-9286
1558-2523
DOI:10.1109/9.284879