Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Piecewise structure of Lyapunov functions and densely checked decrease
  conditions for hybrid systems   We propose a class of locally Lipschitz functions with piecewise structure
for use as Lyapunov functions for hybrid dynamical systems. Subject to some
regularity of the dynamics, we show that Lyapunov inequalities can be checked
only on a dense set and thus we avoid checking them at points of
nondifferentiability of the Lyapunov function. Connections to other classes of
locally Lipschitz or piecewise regular functions are also discussed and
applications to hybrid dynamical systems are included.

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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn