Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polytopic uncertainty for linear systems: New and old complexity results   We survey the problem of deciding the stability or stabilizability of
uncertain linear systems whose region of uncertainty is a polytope. This
natural setting has applications in many fields of applied science, from
Control Theory to Systems Engineering to Biology. We focus on the algorithmic
decidability of this property when one is given a particular polytope. This
setting gives rise to several different algorithmic questions, depending on the
nature of time (discrete/continuous), the property asked
(stability/stabilizability), or the type of uncertainty (fixed/switching).
Several of these questions have been answered in the literature in the last
thirty years. We point out the ones that have remained open, and we answer all
of them, except one which we raise as an open question. In all the cases, the
results are negative in the sense that the questions are NP-hard. As a
byproduct, we obtain complexity results for several other matrix problems in
Systems and Control.

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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: stat