Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Robust Stability of Switched Systems in the Context of Filippov
  Solutions   The stability problem of a class of nonlinear switched systems defined on
compact sets with state-dependent switching is considered. Instead of the
Caratheodory solutions, the general Filippov solutions are studied. This
encapsulates solutions with infinite switching in finite time and sliding modes
in the neighborhood of the switching surfaces. In this regard, a Lyapunov-like
stability theorem, based on the theory of differential inclusions, is
formulated. Additionally, the results are extended to switched systems with
simplical uncertainty. It is also demonstrated that, for the special case of
polynomial switched systems defined on semi-algebraic sets, stability analysis
can be checked based on sum of squares programming techniques.

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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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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: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom