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Proceedings of the American Mathematical Society

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

 

 

A differential equation of Lurie type


Author: T. A. Burton
Journal: Proc. Amer. Math. Soc. 36 (1972), 491-496
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9939-1972-0310334-X
MathSciNet review: 0310334
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Abstract: The problem of Lurie consists of finding necessary and sufficient conditions for all solutions of the system $ \{ x' = Ax + bf(\sigma ),\sigma ' = {c^T}x - rf(\sigma )\} $ to tend to zero as $ t \to \infty $ under appropriate conditions on the functions involved. When $ f(\sigma )/\sigma \to 0$ as $ \vert\sigma \vert \to \infty $, we obtain NASC's for all solutions to be uniformly ultimately bounded.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0310334-X
Keywords: Problem of Lurie, differential equation, boundedness of solutions, control theory
Article copyright: © Copyright 1972 American Mathematical Society