Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Partial Integral Equation (PIE) Representation of Coupled Linear PDEs
  and Scalable Stability Analysis using LMIs   We present a new Partial Integral Equation (PIE) representation of Partial
Differential Equations (PDEs) in which it is possible to use convex
optimization to perform stability analysis with little or no conservatism. The
first result gives a standardized representation for coupled linear PDEs in a
single spatial variable and shows that any such PDE, suitably well-posed,
admits an equivalent PIE representation, defined by the given conversion
formulae. This leads to a new prima facie representation of the dynamics
without the implicit constraints on system state imposed by boundary
conditions. The second result is to show that for systems in this PIE
representation, convex optimization may be used to verify stability without
discretization. The resulting algorithms are implemented in the Matlab toolbox
PIETOOLS, tested on several illustrative examples, compared with previous
results, and the code has been posted on Code Ocean. Scalability testing
indicates the algorithm can analyze systems of up to 40 coupled PDEs on a
desktop computer.

22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph