The real structured singular value is hardly approximable

This paper investigates the problem of approximating the real structured singular value (real /spl mu/). A negative result is provided which shows that the problem of checking if /spl mu/=0 is NP-hard. This result is much more negative than the known NP-hard result for the problem of checking if /sp...

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Bibliographic Details
Published in:IEEE transactions on automatic control 1997-09, Vol.42 (9), p.1286-1288
Main Author: FU, M
Format: Article
Language:English
Subjects:
Applied sciences
Australia Council
Computational complexity
Computer science
control theory
systems
Control system analysis
Control systems
Control theory. Systems
Exact sciences and technology
NP-hard problem
Optimal control
Polynomials
Robust control
Robust stability
Sections
Upper bound
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Summary:This paper investigates the problem of approximating the real structured singular value (real /spl mu/). A negative result is provided which shows that the problem of checking if /spl mu/=0 is NP-hard. This result is much more negative than the known NP-hard result for the problem of checking if /spl mu/0 (even exponential functions of n), unless NP=P. A similar statement holds for the lower bound of /spl mu/. Our result strengthens a recent result by Toker, which demonstrates that obtaining a sublinear approximation for /spl mu/ is NP-hard.
ISSN:0018-9286
1558-2523
DOI:10.1109/9.623094