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A popov criterion for uncertain linear multivariable systems

Authors
Journal
Automatica
0005-1098
Publisher
Elsevier
Publication Date
Volume
31
Issue
7
Identifiers
DOI: 10.1016/0005-1098(95)00025-r
Keywords
  • Popov Criterion
  • Uncertain Dynamic Systems
  • Robust Stability
  • Structured Singular Value

Abstract

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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