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

Datko教授将研究时间延迟对一些无限维系统的稳定边界控制的影响。将考虑三个方面。(i)小时间延迟对双曲型偏微分方程描述的系统的稳定控制的影响。（ii）粘弹性系统相对于弹性系统存在时滞时稳定性的鲁棒性。在某些情况下，当将时间延迟引入前者的阻尼时，前者似乎不如后者敏感。因此，粘弹性系统可以作为比弹性系统更合适的柔性结构模型。（iii）重新检查弹性系统的可控性和稳定性，以期考虑这些概念的“近似”定义，这些概念对涉及时滞的扰动具有鲁棒性。

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.