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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A Liapunov function for three-dimensional feedback systems


Author: Ji Fa Jiang
Journal: Proc. Amer. Math. Soc. 114 (1992), 1009-1013
MSC: Primary 93D15; Secondary 34C11
DOI: https://doi.org/10.1090/S0002-9939-1992-1092922-1
MathSciNet review: 1092922
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Abstract: For a three-dimensional model of a positive feedback loop, Selgrade [11, 12] proved that every positive-time trajectory in the nonnegative orthant converges. Hirsch [6] gave another proof of this result under slightly different assumptions. This paper provides a new proof of Selgrade's result that is much shorter and presents a generalization that can be applied to positive and negative feedback loops and other systems.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1092922-1
Keywords: Positive and negative feedback systems, convergence, Liapunov function
Article copyright: © Copyright 1992 American Mathematical Society