Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bode's Sensitivity Integral Constraints: The Waterbed Effect in Discrete
  Time   Bode's sensitivity integral constraints define a fundamental rule about the
limitations of feedback and is referred to as the waterbed effect. In a
companion paper, we took a fresh look at this problem using a direct approach
to derive our results. In this paper, we will address the same problem, but now
in discrete time. Although similar to the continuous case, the discrete-time
case poses its own peculiarities and subtleties. The main result is that the
sensitivity integral constraint is crucially related to the locations of the
unstable open-loop poles of the system. This makes much intuitive sense.
Similar results are also derived for the complementary sensitivity function. In
that case the integral constraint is related to the locations of the
transmission zeros outside the unit circle. Hence all performance limitations
are inherently related to the open-loop poles and the transmission zeros
outside the unit circle. A number of illustrative examples are presented.

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The categories of this paper are: math
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga