Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\mathcal{H}_2$-gap model reduction for stabilizable and detectable
  systems   We formulate here an approach to model reduction that is well-suited for
linear time-invariant control systems that are stabilizable and detectable but
may otherwise be unstable. We introduce a modified $\mathcal{H}_2$-error
metric, the $\mathcal{H}_2$-gap, that provides an effective measure of model
fidelity in this setting. While the direct evaluation of the
$\mathcal{H}_2$-gap requires the solutions of a pair of algebraic Riccati
equations associated with related closed-loop systems, we are able to work
entirely within an interpolatory framework, developing algorithms and
supporting analysis that do not reference full-order closed-loop Gramians. This
leads to a computationally effective strategy yielding reduced models designed
so that the corresponding reduced closed-loop systems will interpolate the
full-order closed-loop system at specially adapted interpolation points,
without requiring evaluation of the full-order closed-loop system nor even
computation of the feedback law that determines it. The analytical framework
and computational algorithm presented here provides an effective new approach
toward constructing reduced-order models for unstable systems. Numerical
examples for an unstable convection diffusion equation and a linearized
incompressible Navier-Stokes equation illustrate the effectiveness of this
approach.

31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc