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Computational complexity of real structured singular value in ℓp setting
Conference proceeding

Computational complexity of real structured singular value in ℓp setting

Minyue Fu and Soura Dasgupta
1997 European Control Conference (ECC), pp.3452-3455
European Conrol Conference (Brussels, Belgium, 07/01/1997–07/07/1997)
07/1997
DOI: 10.23919/ECC.1997.7082647

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Abstract

This paper studies the structured singular value (μ) problem with real parameters bounded by an ℓ p norm. Our main result shows that this generalized μ problem is NP-hard for any given rational number p ϵ [1, ∞], whenever k, the size of the smallest repeated block, exceeds 1. This result generalizes the known result that the conventional μ problem (with p - ∞) is NP-hard. However, our proof technique is different from the known proofs for the p - ∞ case as these proofs do not generalize to p ≠ ∞. For k - 1 and p - ∞, the μ problem is known to be NP-hard. We provide an alternative proof of this result. For k = 1 and p finite the issue of NP-hardness remains unresolved. When every block has size 1, and p - 2 we outline some potential difficulties in computing μ.
Control Systems Polynomials Computational complexity Computers Periodic structures robust stability analysis Structured singular value Transforms Uncertainty

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