Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: When multiplicative noise stymies control   We consider the stabilization of an unstable discrete-time linear system that
is observed over a channel corrupted by continuous multiplicative noise. Our
main result shows that if the system growth is large enough, then the system
cannot be stabilized in a second-moment sense. This is done by showing that the
probability that the state magnitude remains bounded must go to zero with time.
Our proof technique recursively bounds the conditional density of the system
state (instead of focusing on the second moment) to bound the progress the
controller can make. This sidesteps the difficulty encountered in using the
standard data-rate theorem style approach; that approach does not work because
the mutual information per round between the system state and the observation
is potentially unbounded.
  It was known that a system with multiplicative observation noise can be
stabilized using a simple memoryless linear strategy if the system growth is
suitably bounded. In this paper, we show that while memory cannot improve the
performance of a linear scheme, a simple non-linear scheme that uses one-step
memory can do better than the best linear scheme.

24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin