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

MathSciNet review:
1092922

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

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