Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of interconnected impulsive systems with and without
  time-delays using Lyapunov methods   In this paper we consider input-to-state stability (ISS) of impulsive control
systems with and without time-delays. We prove that if the time-delay system
possesses an exponential Lyapunov-Razumikhin function or an exponential
Lyapunov-Krasovskii functional, then the system is uniformly ISS provided that
the average dwell-time condition is satisfied. Then, we consider large-scale
networks of impulsive systems with and without time-delays and we prove that
the whole network is uniformly ISS under a small-gain and a dwell-time
condition. Moreover, these theorems provide us with tools to construct a
Lyapunov function (for time-delay systems - a Lyapunov-Krasovskii functional or
a Lyapunov-Razumikhin function) and the corresponding gains of the whole
system, using the Lyapunov functions of the subsystems and the internal gains,
which are linear and satisfy the small-gain condition. We illustrate the
application of the main results on examples.

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The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
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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: econ
10
The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: cs