Genericity of non-degenerate policies in H-infinity control

Let $\mathcal{C}_n$ be the space of full-order dynamic policies, and let $\mathcal{C}_{\mathrm{nd}}$ be the subset of non-degenerate policies, namely those admitting a certificate $P\in\mathbb{S}^{2n}_{++}$ whose off-diagonal block $P_{12}$ lies in $\mathrm{GL}_n$ and satisfies the bounded-real matrix inequality at the policy's $\mathcal{H}_\infty$ cost. Genericity conjecture. The complement

$$\mathcal{C}_n\backslash\mathcal{C}_{\mathrm{nd}}$$

has measure zero in the space $\mathbb{R}^{(m+n)\times(p+n)}$. Unlike the smooth LQG case, this remains open because the nonsmoothness of the $\mathcal{H}_\infty$ cost prevents a direct real-analytic zero-set argument.