5 problems

Russell–Weiss conjecture. The Hautus test is sufficient for exact controllability of the system.

Let the autonomous time-delay system be given on the history space $\mathcal X^n$. It is forward complete if every solution exists for all positive times, and it is robustly forwar…

Let $T(N,s)$ be the recursively defined integer matrix family described in the source, acting by discrete iteration $x_n=T^nx$ on vectors with a continuous spatial-coordinate inter…

The time-domain input-output conjecture. The input-output map is given by

Unbounded-operator stability conjecture. An unbounded operator in the controller will help achieve better stability properties for the closed-loop system, especially when the close…