&amp;#x2112;&lt;inf&gt;2&lt;/inf&gt; gain bounds for systems with slope-restricted nonlinearities

SUMMARYThis paper proposes an LMI-based approach for studying the stability of feedback interconnections of a finite dimensional LTI system and a nonlinear element that consists of several identical scalar nonlinearities that have restrictions on their sector and slope. The results are based on the integral quadratic constraint stability analysis framework and other recent results that give a sharp characterisation of stability multipliers for monotone, repeated scalar nonlinearities. Several examples show the effectiveness of the proposed approach; the lack of conservatism in the results is noteworthy.

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Tractable stability analysis for systems containing repeated scalar slope‐restricted nonlinearities

Turner

Kerr

Sofrony

2013

Intl J Robust & Nonlinear

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Absolute stability analysis for negative-imaginary systems

2016

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Applying negative imaginary systems theory to non-square systems with polytopic uncertainty

Bhowmick

Lanzon

2021

Automatica

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ℒ<inf>2</inf> gain bounds for systems with slope-restricted nonlinearities

Cited by 9 publications

References 19 publications

Tractable stability analysis for systems containing repeated scalar slope‐restricted nonlinearities

Tractable stability analysis for systems containing repeated scalar slope‐restricted nonlinearities

Absolute stability analysis for negative-imaginary systems

Applying negative imaginary systems theory to non-square systems with polytopic uncertainty

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