Analysis of Systems With Slope Restricted Nonlinearities Using Externally Positive Zames-Falb Multipliers

This paper proposes an approach for assessing the stability of feedback interconnections where one element is a static slope-restricted nonlinearity and the other element is a linear system. The approach is based on the use of Zames-Falb multipliers where the dynamic portion of the multiplier is cho...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2020-04, Vol.65 (4), p.1660-1667
Main Authors: Turner, Matthew C., Drummond, Ross
Format: Article
Language:English
Subjects:
Asymptotic stability
Frequency-domain analysis
Linear matrix inequalities
Linear matrix inequality (LMI)
Mathematical analysis
Multipliers
Parameterization
single-input-single-output (SISO)
Stability analysis
Stability criteria
Symmetric matrices
Time-domain analysis
Transfer functions
Zames-Falb multipliers
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Summary:This paper proposes an approach for assessing the stability of feedback interconnections where one element is a static slope-restricted nonlinearity and the other element is a linear system. The approach is based on the use of Zames-Falb multipliers where the dynamic portion of the multiplier is chosen as an externally positive noncausal transfer function. By restricting attention to a subset of these multipliers, a set of pure linear matrix inequality conditions is obtained which requires no initial parameterization by the user. A useful byproduct of using externally positive systems is that the results are applicable to nonodd slope restricted nonlinearities, which is not the case for all classes of Zames-Falb multipliers.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2019.2930796