Computational complexity of μ calculation
Richard D. Braatz,Peter M. Young,John Doyle,Manfred Morari +3 more
- pp 1682-1683
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It is proved that the μ recognition problem with either pure real or mixed real/complex uncertainty is NP-hard, which strongly suggests that it is futile to pursue exact methods for calculating μ of general systems with purereal or mixed uncertainty for other than small problems.Abstract:
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.read more
Citations
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Robust control of uncertain systems: Classical results and recent developments
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The boundedness of all products of a pair of matrices is undecidable
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A Convex Approach to Robust Stability for Linear Systems with Uncertain Scalar Parameters
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Randomized algorithms for probabilistic robustness with real and complex structured uncertainty
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References
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Checking robust nonsingularity is NP-hard
Svatopluk Poljak,Jiří Rohn +1 more
TL;DR: It is shown that the question of whether A0+r1A1+···+rkAk is nonsingular for all possible choices of real numbersr1, ...,rk in the interval [0, 1].
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Continuity properties of the real/complex structured singular value
Andrew Packard,P. Pandey +1 more
TL;DR: It is shown that mu is always upper semi-continuous, and conditions are derived under which it is also lower semi- Continuing, which means the real-parameter robustness problem is reexamined.