2001
DOI: 10.1109/9.956057
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Conservatism of the circle criterion-solution of a problem posed by A. Megretski

Abstract: In the collection of open problems in mathematical systems and control theory [1] Alexandre Megretski posed a problem from which it follows how conservative the well-known circle criterion may be. We solve this problem.

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Cited by 4 publications
(3 citation statements)
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“…(1)]) notes the importance of relating the multiplication operation in the time domain and the frequency domain. This problem is also considered in [8]. Theorem 3.1 may provide insight into this relationship.…”
Section: Mathematical Preliminariesmentioning
confidence: 99%
“…(1)]) notes the importance of relating the multiplication operation in the time domain and the frequency domain. This problem is also considered in [8]. Theorem 3.1 may provide insight into this relationship.…”
Section: Mathematical Preliminariesmentioning
confidence: 99%
“…n--+oo M*(Mn) , which implies that the circle criterion cannot be sharp up to a constant that does not depend on the order of a system. Note that the argument of [15] also holds for the cases when the whose inverse also provides a lower bound on the robust stability margin for the M-� feedback interconnected system with the nonlinear operator r in the place of �, which is denoted by l/M * (M). It is not known whether there exists a sequence of matrices Mn E c n x n such that (16) This Popov criterion can be extended to norm-bounded real para metric uncertain matrices and provides an upper bound on the structured singular value with real parametric uncertainties [45], [46].…”
Section: A Absolute Stabilitymentioning
confidence: 97%
“…The greater ease in the computation of upper bounds on M motivated the analysis of their conservatism, which was investigated by Alexandre Megretski and others [11]- [15].…”
Section: Introductionmentioning
confidence: 99%