6 problems

Periodic-solution conjecture. If all solutions are uniform-bounded and uniform ultimate-bounded, then there exists a nonzero periodic solution with period $T$, which need not be un…

OZF multiplier conjecture. If such a multiplier exists, then $y_2\in\mathcal{L}_2\cap\mathcal{L}_{\infty}$.

Altshuller multiplier conjecture. If such a multiplier exists, then there exists a nonzero periodic solution with period $T$, which need not be unique or attracting.

Let $G$ be a stable transfer function, let $k_N$ be its Nyquist value, and let $\phi$ be a memoryless nonlinearity in $S[0,k]$. Kalman conjecture. The feedback interconnection of…

Kalman's convergence-rate conjecture. For any stable $G$ and $\Delta\in S[0,K]$ with $K<K_N$,

Small-perturbation solvability conjecture. Whenever $\lVert\vec{\epsilon}\rVert$ is sufficiently small, this system has a solution