Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the solvability of the Yakubovich linear-quadratic infinite horizon
  minimization problem   The Yakubovich Frequency Theorem, in its periodic version and in its general
nonautonomous extension, establishes conditions which are equivalent to the
global solvability of a minimization problem of infinite horizon type, given by
the integral in the positive half-line of a quadratic functional subject to a
control system. It also provides the unique minimizing pair "solution, control"
and the value of the minimum. In this paper we establish less restrictive
conditions under which the problem is partially solvable, characterize the set
of initial data for which the minimum exists, and obtain its value as well a
minimizing pair. The occurrence of exponential dichotomy and the null character
of the rotation number for a nonautonomous linear Hamiltonian system defined
from the minimization problem are fundamental in the analysis.

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The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
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The categories of this paper are: stat
31
The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
7
The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga