Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential stabilization of cascade ode-reaction-diffusion pde by
  pointwise actuation   In this paper, we are concerned with the state feedback stabilization of
ODE-PDE cascade systems governed by a linear ordinary differential equation and
the 1-d reaction-diffusion equation posed on a bounded interval. In contrast to
the previous works in the literature where the control acts at the boundary,
the control for the entire system acts at an inside point of the PDE domain
whereas the PDE acts in the linear ODE by a Neumann connection. We use the
infinite dimensional backstepping design to convert system under consideration
to an exponentially target system. By invertibility of the design and Lyapunov
analysis, we prove the well posedness and exponential stability of such system.

23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an