11 problems

Consider a time-delay system with an input-to-state stability (ISS) Lyapunov-Krasovskii functional (LKF), whose dissipation is expressed in terms of the norm of the current solutio…

No-relaxation-gap conjecture. There is no relaxation gap between the trajectory formulation … , so that $p^*=P^*$.

Consider the time-delay system on $\mathcal X^n$ with inputs in $\mathcal U^m$. 0-GAS plus BEFBS conjecture. Assume the system is 0-GAS and, for some $\zeta\in\mathcal K_\infty$, e…

Consider the time-delay system on $\mathcal X^n$ with inputs in $\mathcal U^m$. Converse point-wise iISS-LKF conjecture. If the system is iISS, then it admits an iISS Lyapunov–Kras…

Let the time-delay system act on $\mathcal X^n$ with inputs in $\mathcal U^m$. Assume that there are $\alpha,\overline\alpha\in\mathcal K_\infty$ and $\gamma\in\mathcal N$ such tha…

Consider the time-delay system on $\mathcal X^n$ with inputs in $\mathcal U^m$. 0-GAS plus point-wise ULIM conjecture. If the system is 0-GAS and satisfies the point-wise version o…

ISS under point-wise dissipation conjecture. These assumptions imply that the system is ISS. The converse is known, so this would provide an alternative characterization of ISS and…

GES under point-wise dissipation conjecture. Under these assumptions, the system is GES. The converse is known from the cited theorem, so the conjecture would characterize GES thro…

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 the autonomous time-delay system be given on the history space $\mathcal X^n$, with solution $x(t,x_0)$ from initial history $x_0$. GAS conjecture. The system is GAS if and onl…

Consider the neutral-type time-delay system described by the characteristic matrix … Here $A_{-1}$ is the neutral-delay matrix, $A_2$ and $A_3$ are the delay kernels, and $b$ is th…