Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalent Stability Notions, Lyapunov Inequality, and Its Application
  in Discrete-Time Linear Systems with Stochastic Dynamics Determined by an
  i.i.d. Process   This paper is concerned with stability analysis and synthesis for
discrete-time linear systems with stochastic dynamics. Equivalence is first
proved for three stability notions under some key assumptions on the randomness
behind the systems. In particular, we use the assumption that the stochastic
process determining the system dynamics is independent and identically
distributed (i.i.d.) with respect to the discrete time. Then, a Lyapunov
inequality condition is derived for stability in a necessary and sufficient
sense. Although our Lyapunov inequality will involve decision variables
contained in the expectation operation, an idea is provided to solve it as a
standard linear matrix inequality; the idea also plays an important role in
state feedback synthesis based on the Lyapunov inequality. Motivating numerical
examples are further discussed as an application of our approach.

9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc