Minimal stationary policies are non-degenerate in H-infinity control

Let $\mathcal{C}_n$ be the space of full-order dynamic policies for $\mathcal{H}_\infty$ control. A policy $\mathsf{K}\in\mathcal{C}_n$ is Clarke stationary when $0\in\partial J_{\infty,n}(\mathsf{K})$, and a minimal policy is a policy of minimal controller order. A non-degenerate policy is one belonging to $\mathcal{C}_{\mathrm{nd}}$, the class admitting a positive-definite Lyapunov certificate with invertible off-diagonal block. Minimal-policy conjecture. If $\mathsf{K}\in\mathcal{C}_n$ is a Clarke stationary point and is a minimal policy, then it is non-degenerate, and hence it is a global minimum of $J_{\infty,n}(\mathsf{K})$ over $\mathcal{C}_n$. The claim is presented as an analogue of the LQG result; its resolution is left to future work, and the supplied status evidence marks it as disproved.