The closed-loop matrix of a dynamical system is an anti-triangular block matrix of the form
$$ A_\mathrm{cl} = \begin{bmatrix} A & BS \\ -\epsilon \left( G_u S \right)^\top {M} C & 0 \end{bmatrix} $$
where the matrix $A$ is Hurwitz, the matrix $G_u$ is full-column rank, the matrix $M$ is diagonal and positive definite ($M \succ 0$). Prove that the dynamical system is stable, i.e., that $A_\mathrm{cl}$ is Hurwitz.
Can we say anything about the eigenvalues of $A_\mathrm{cl}$? Any theory or discussion would be helpful!