Mathematical Sciences: An Investigation of the Effect of Small Time Delays in the Boundary Control of Hyperbolic Partial Differential Equations

达特科教授将研究 稳定边界控制的时滞 无限维系统 三个领域将 考虑了(i)小时间延迟对 双曲型系统的稳定控制 偏微分方程(ii)的鲁棒性 粘弹性系统的稳定性， 维斯维斯弹性系统的时间延迟。 前 在某些情况下，似乎不如 当时间延迟被引入到它们的 阻尼 因此，粘弹性系统可以用作更多的 柔性结构比弹性结构更适合的模型 系统. (iii)重新审视可控性和 弹性系统的可稳定性， 考虑到这些概念的“近似”定义 其相对于扰动是鲁棒的， 时间延迟

Professor Datko will investigate the effects of time delays on stabilizing boundary controls of some infinite-dimensional systems. Three areas will be considered. (i) The effects of small time delays on stabilizing controls for systems described by hyperbolic partial differential equations. (ii) The robustness of the stability of viscoelastic systems in the presence of time delays vis a vis elastic systems. The former appear, in some cases, to be less sensitive than the latter when time delays are introduced into their damping. Hence viscoelastic systems may serve as more suitable models for flexible structures than elastic systems. (iii) A reexamination of controllability and stabilizability for elastic systems with a view to considering "approximate" definitions of these concepts which are robust with respect to perturbations involving time delays.