7 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…

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…

The exact discrete-time model and an approximate discrete-time model are compared through the one-step consistency property REPC, which is sufficient for the multistep consistency…

The paper considers a function $f$ whose Hessian satisfies a global upper bound, an assumption used in an earlier theorem to establish an ISS Lyapunov function. Relaxation conjectu…

Let $m$ denote the measurement noise in the plant, and consider the decentralized consensus algorithm in equation … . ISS-like robustness conjecture. When $m$ is not zero, the algo…