Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Delay-independent stability in monotone systems   Monotone systems comprise an important class of dynamical systems that are of
interest both for their wide applicability and because of their interesting
mathematical properties. It is known that under the property of
quasimonotonicity time-delayed systems become monotone, and some remarkable
properties have been reported for such systems. These include, for example, the
fact that for linear systems global asymptotic stability of the undelayed
system implies global asymptotic stability for the delayed system under
arbitrary bounded delays. Nevertheless, extensions to nonlinear systems have
thus far relied primarily on the conditions of homogeneity and subhomogeneity,
and it has been conjectured that these can be relaxed. Our aim in this paper is
to show that this is feasible for a general class of nonlinear monotone systems
by deriving convergence results in which simple properties of the undelayed
system lead to delay-independent stability. In particular, one of our results
shows that if the undelayed system has a convergent trajectory that is
unbounded in all components as $t \to -\infty$, then the system is globally
asymptotically stable for arbitrary bounded time-varying delays. This follows
from a more general result derived in the paper that allows to quantify
delay-independent regions of attraction, which can be used to prove global
asymptotic stability for various classes of systems. These also recover various
known delay-independent stability results that are discussed within the paper.

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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: stat