Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robustness of Safety for Linear Dynamical Systems: Symbolic and
  Numerical Approaches   In this paper, we study the robustness of safety properties of a linear
dynamical system with respect to model uncertainties. Our paper involves three
parts. In the first part, we provide symbolic (analytical) and numerical
(representation based) techniques for computing the reachable set of uncertain
linear systems. We further prove a relationship between the reachable set of a
linear uncertain system and the maximum singular value of the uncertain
dynamics matrix. Finally, we propose two heuristics to compute the robustness
threshold of the system -- the maximum uncertainty that can be introduced to
the system without violating the safety property. We evaluate the reachable set
computation techniques, effects of singular values, and estimation of
robustness threshold on two case studies from varied domains, illustrating the
applicability, practicality and scalability of the artifacts, proposed in this
paper, on real-world examples. We further evaluate our artifacts on several
linear dynamical system benchmarks. To the best of the authors' knowledge, this
is the first work to: (i) extend perturbation theory to compute reachable sets
of linear uncertain systems, (ii) leverage the relationship between the
reachable set of a linear system and the maximum singular values to determine
the effect of uncertainties and (3) estimate the threshold of robustness that
can be tolerated by the system while remaining safe.

18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
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The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph