5 problems

Output-Lagrange stability and output asymptotic gain imply OL-IOS. Under these assumptions, the system is OL-IOS.

Let $\Sigma(A,[0,B_1])$ and $\Sigma(A,[0,B_2])$ denote the two linear systems associated with a bilinear system, and suppose that the bilinear system satisfies the hypothesis of Se…

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…