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 , and , where , such that
.
Moreover, for every that satisfies
,
and are solutions to