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Title: On the Existence of Stable, Causal Multipliers for Systems With Slope-Restricted Nonlinearities
Authors: Turner, Matthew C.
Kerr, M. L.
Postlethwaite, Ian
First Published: Nov-2009
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Citation: IEEE Transactions on Automatic Control, 2009, 54 (11), pp. 2697-2702.
Abstract: The stability of a feedback interconnection of a linear time invariant (LTI) system and a slope-restricted nonlinearity is revisited. Unlike the normal treatment of this problem, in which multipliers are explicitly chosen and then stability conditions checked, this technical note derives existence conditions for a sub-class of these multipliers, namely those which are $ {cal L}_{1}$ bounded, stable, causal and of order equal to the LTI part of the system. It is proved that for the single-input-single-output case, these existence conditions can be expressed as a set of linear matrix inequalities and thus can be solved efficiently with modern optimization software. Examples illustrate the effectiveness of the results.
DOI Link: 10.1109/TAC.2009.2031581
ISSN: 0018-9286
Type: Article
Rights: This paper was published as IEEE Transactions on Automatic Control, 2009, 54 (11), pp. 2697-2702. It is available from Doi: 10.1109/TAC.2009.2031581. Copyright © 2009 IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Leicester’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
Appears in Collections:Published Articles, Dept. of Engineering

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