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Computation of the Structured Singular Value via Moment LMI Relaxations

Piga, Dario Computation of the Structured Singular Value via Moment LMI Relaxations. IEEE Transactions on Automatic Control. ISSN 0018-9286 (In Press)

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Abstract

The Structured Singular Value (SSV) provides a powerful tool to test robust stability and performance of feedback systems subject to structured uncertainties. Unfortunately, computing the SSV is an NP-hard problem, and the polynomial-time algorithms available in the literature are only able to provide, except for some special cases, upper and lower bounds on the exact value of the SSV. In this work, we present a new algorithm to compute an upper bound on the SSV in case of mixed real/complex uncertainties. The underlying idea of the developed approach is to formulate the SSV computation as a (nonconvex) polynomial optimization problem, which is relaxed into a sequence of convex optimization problems through moment-based relaxation techniques. Two heuristics to compute a lower bound on the SSV are also discussed. The analyzed numerical examples show that the developed approach provides tighter bounds than the ones computed by the algorithms implemented in the Robust Control Toolbox in Matlab, and it provides, in most of the cases, coincident lower and upper bounds on the structured singular value.

Item Type: Article
Identification Number: 10.1109/TAC.2015.2438452
Subjects: T Technology > T Technology (General)
Research Area: Computer Science and Applications
Depositing User: Dario Piga
Date Deposited: 26 Oct 2015 12:27
Last Modified: 26 Oct 2015 12:27
URI: http://eprints.imtlucca.it/id/eprint/2784

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