Consider the set of matrices A = {
}
Every matrix in the set A is Hurwitz if and only if there exist
, i = 1, 2, 3, 4, where Pi > 0,
i = 1, 2, 3, 4, such that
![{\displaystyle {\begin{aligned}\qquad P_{i}A_{i}+A_{i}^{T}P_{i}<0\qquad i=1,2,3,4,\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/79d689444bb04d356d5e06bf519d491485757753)
where
Equivalently, every matrix in the set A is Hurwitz if and only if there exist
, i = 1, 2, 3, 4,
where Qi > 0, i = 1, 2, 3, 4, such that
![{\displaystyle {\begin{aligned}\qquad A_{i}Q_{i}+Q_{i}A_{i}^{T}<0\qquad i=1,2,3,4,\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c578e70381c4c301b51494a119452fb5bd25434b)