On the Kamke-Muller conditions, monotonicity and continuity for bi-modal piecewise-smooth systems

O'Donoghue, Yoann and Mason, Oliver and Middleton, Rick (2012) On the Kamke-Muller conditions, monotonicity and continuity for bi-modal piecewise-smooth systems. Systems and Control Letters, 61 (1). pp. 180-186. ISSN 0167-6911

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We show that the Kamke-Muller conditions for bimodal piecewise-smooth systems are equivalent to simple conditions on the vector elds dening the system. As a consequence, we show that for a specic class of such systems, monotonicity is equivalent to continuity. Furthermore, we apply our results to derive a stability condition for piecewise positive linear systems.

Item Type: Article
Additional Information: Notice: this is the author’s version of a work that was accepted for publication in Systems & Control Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Systems & Control Letters, [Vol.61, No.1, (2012)] DOI: http://dx.doi.org/10.1016/j.sysconle.2011.10.015
Keywords: Piecewise-smooth systems; monotone systems; positive systems stability; Kamke-Muller conditions;
Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID: 3750
Depositing User: Oliver Mason
Date Deposited: 13 Jun 2012 14:09
Journal or Publication Title: Systems and Control Letters
Publisher: Elsevier
Refereed: Yes

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