Discrete-time off-axis circle criterion conjecture

Consider a feedback system with $G\in\mathbf{RH}_\infty$, and let $c6$ be slope-restricted in $S[0,k]$ and monotonically increasing. The Nyquist plot of the linear part is the plot of $G(e^{j\omega})$. Discrete-time off-axis circle criterion conjecture. If this Nyquist plot lies entirely to the right of a straight line passing through $(-1/k+\delta,0)$, where $\delta>0$, then the feedback interconnection is $ell_2$-stable. The paper states that this conjecture is false in general, although the corresponding continuous-time theorem is true.