Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linearizations for Rosenbrock system polynomials and rational matrix
  functions   Our aim in this paper is two-fold: First, for computing zeros of a linear
time-invariant (LTI) system $\Sigma$ in {\em state-space form}, we introduce a
"trimmed structured linearization", which we refer to as {\em Rosenbrock
linearization}, of the Rosenbrock system polynomial $\mathcal{S}(\lam)$
associated with $\Sigma.$ We also introduce Fiedler-like matrices for
$\mathcal{S}(\lam)$ and describe constructions of Fiedler-like pencils for
$\mathcal{S}(\lam).$ We show that the Fiedler-like pencils of
$\mathcal{S}(\lam)$ are Rosenbrock linearizations of the system polynomial
$\mathcal{S}(\lam).$ Second, with a view to developing a direct method for
solving rational eigenproblems, we introduce "linearization" of a rational
matrix function. We describe a state-space framework for converting a rational
matrix function $G(\lam)$ to an "equivalent" matrix pencil $\mathbb{L}(\lam)$
of smallest dimension such that $G(\lam)$ and $\mathbb{L}(\lam)$ have the same
"eigenstructure" and we refer to such a pencil $\mathbb{L}(\lam)$ as a
"linearization" of $G(\lam).$ Indeed, by treating $G(\lam)$ as the transfer
function of an LTI system $\Sigma_G$ in state-space form via state-space
realization, we show that the Fiedler-like pencils of the Rosenbrock system
polynomial associated with $\Sigma_G$ are "linearizations" of $G(\lam)$ when
the system $\Sigma_G$ is both controllable and observable.

25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics