Consider
. The matrix
is
-stable if and only if there exists
, where
, such that
,
or equivalent
,
where
is the Kroenecker product,
The eigenvalues of a
-stable matrix lie within the LMI region
, which is defined as
, where
,
,
, and
is the complex conjugate of
.
Consider
and
. The matrix
satisfies
, where
if and only if there exist
and
, where
, such that
.
Equivalently, the matrix
satisfies
if and only if there exist
,
, and
, where
, such that
.
Moreover, for every
that satisfies
and
are solutions to
.