On several variable zero sets and application to MIMO robust feedback stabilization

Given a complex-valued function
f
which depends on
m
real variables
s_1,\cdots,s_m
and
n
complex parameters
A_1,\cdots,A_n
, we describe a method of finding the zero set
V
of all zeros of
f
in some given set
G
in
R^m
when each parameter
A_i
is allowed to vary in some given set
K_i
in the extended complex plane
\overline{\bf C} = {\bf C} \cup{\infty}
. This mathematical tool is applied in the paper to determine the complete space of output (or state) feedback gains, which allows robust stabilization of a linear MIMO system under uncertainty conditions. The system may be continuous or discrete. Also, the stabilization may be "relative," i.e., with safety margins. Design examples are provided.