论文标题
关于时间延迟系统的稳定性的推导，对初始条件的时间衍生而没有约束
On the derivation of stability properties for time-delay systems without constraint on the time-derivative of the initial condition
论文作者
论文摘要
延迟微分方程的稳定性与Lyapunov-Krasovskii功能的存在密切相关。即使已经报道了有关此类功能的存在的许多相反结果，也缺乏用于选择的建设性方法。对于缺乏这种建设性方法的某些类别的时间延迟系统，这表明lyapunov-krasovskii功能也允许依赖状态 - 标题的时间衍生功能，是研究稳定性特性的有效工具。但是，在这种方法中，必须将初始条件与正方形的弱衍生物绝对连续。此外，根据初始条件及其时间衍生的大小进行评估的初始条件的稳定性结果。本文的主要目的是表明，对于某些类别的时间延迟系统，上述稳定结果实际上可以扩展到仅假定连续且以统一标准评估的初始条件。
Stability of retarded differential equations is closely related to the existence of Lyapunov-Krasovskii functionals. Even if a number of converse results have been reported regarding the existence of such functionals, there is a lack of constructive methods for their selection. For certain classes of time-delay systems for which such constructive methods are lacking, it was shown that Lyapunov-Krasovskii functionals that are also allowed to depend on the time-derivative of the state-trajectory are efficient tools for the study of the stability properties. However, in such an approach the initial condition needs to be assumed absolutely continuous with a square integrable weak derivative. In addition, the stability results hold for initial conditions that are evaluated based on the magnitude of both the initial condition and its time-derivative. The main objective of this paper is to show that, for certain classes of time-delay systems, the aforementioned stability results can actually be extended to initial conditions that are only assumed continuous and that are evaluated in uniform norm.
