Is this a Hurwitz matrix?

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I have the following block matrix

$$J = \begin{bmatrix}A & B \\ C &D\end{bmatrix}$$

where $A, B, C, D$ are $2 \times 2$ matrices and

1.$A$ is Hurwitz and $a_{ii} < 0$

2. $B = \operatorname{diag}(b_1, b_2)$ with $b_i < 0$.

3. $C = \operatorname{diag}(c_1, c_2)$ with $c_i> 0$.

4. $D = \operatorname{diag}(d_1,d_2)$ with $d_i < 0$.

Is there some necessary and/or sufficient condition on $B, C, D$ for J to be Hurwitz?

$\endgroup$ 4 Sorted by: Reset to default

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