On the existence of stable, causal multipliers for systems with slope-restricted nonlinearities

Turner, Matthew, Kerr, Murray and Postlethwaite, Ian (2009) On the existence of stable, causal multipliers for systems with slope-restricted nonlinearities. IEEE Transactions on Automatic Control, 54 (11). pp. 2697-2702. ISSN 0018-9286

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Official URL: http://dx.doi.org/10.1109/TAC.2009.2031581

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 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.

Item Type: Article
Uncontrolled Keywords: linear time invariant systems
Subjects: H900 Others in Engineering
Department: Faculties > Engineering and Environment > Mathematics and Information Sciences
Depositing User: EPrints Services
Date Deposited: 11 May 2010 08:17
Last Modified: 10 Aug 2015 11:25
URI: http://nrl.northumbria.ac.uk/id/eprint/513

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