Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lyapunov functions: necessary and sufficient conditions for practical
  stability   We prove the necessary and sufficient conditions for practical stability of
nonlinear dynamical system at general phase restrictions. In such a case the
Lyapunov function is nondifferentiable. But if the set of initial data is
starry compact, then it is possible building Lyapunov function which belongs to
differentiable functions class. We also estimate the optimal sets of initial
conditions in structural forms for linear system and concrete phase
restrictions.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
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The categories of this paper are: astro-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ