Abstract
The Popov absolute stability criterion is traditionally proved using a Lyapunov function and the positive real lemma. In this paper a simplified proof of the multivariable Popov criterion is given for the case of one-sided, sector-bounded real parameter uncertainty. A loop-shifting transformation is then used to extend the Popov criterion to two-sided, sector-bounded uncertain matrices. Specialization of this result to norm-bounded uncertain matrices leads to an upper bound for the structured singular value for block-structured, real parameter uncertainty.
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