Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact Instability Margin Analysis and Minimum Norm Strong Stabilization
  -- phase change rate maximization --   This paper is concerned with a new control related optimization problem named
"phase change rate maximization" for single-input-single-output (SISO) linear
time-invariant (LTI) systems. The problem relates to two control problems,
namely robust instability analysis against stable perturbations and minimum
norm strong stabilization. We define an index of the instability margin called
"robust instability radius (RIR)" as the smallest $H_\infty$ norm of a stable
perturbation that stabilizes a given unstable system. This paper has two main
contributions. It is first shown that the problem of finding the exact RIR can
be transformed into a problem of maximizing the phase change rate at the peak
frequency with a phase constraint. Then, we show that the maximum is attained
by a first-order all-pass function and derive conditions, under which the RIR
can be exactly characterized, in terms of the phase change rate. Two extensions
with illustrative examples are also provided.

25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an