论文标题
全球指数稳定性的增长条件和在重点耗散下的时间延迟系统的实验
Growth conditions for global exponential stability and exp-ISS of time-delay systems under point-wise dissipation
论文作者
论文摘要
对于时间延迟系统，众所周知，通过存在Lyapunov-Krasovskii功能，可以保证全球渐近稳定性，该功能以沿解决方案的范围方式消散，即其耗散速率仅涉及解决方案规范的当前价值。到目前为止，将此结果扩展到全球指数稳定性（GES）仅适用于由全球Lipschitz向量领域统治的系统，并且在很大程度上开放了投入到国家稳定性（ISS）属性。在本文中，我们依靠指数ISS的概念来扩展可以从点耗散耗散的GES或ISS的系统类别。反过来，我们的结果表明，在涉及整个状态历史规范的足够小的额外术语的情况下，这些属性仍然存在。我们提供了该额外术语的可容忍幅度的明确估计，并通过一个示例显示了如何使用它来评估建模不确定性的稳健性。
For time-delay systems, it is known that global asymptotic stability is guaranteed by the existence of a Lyapunov-Krasovskii functional that dissipates in a point-wise manner along solutions, namely whose dissipation rate involves only the current value of the solution's norm. So far, the extension of this result to global exponential stability (GES) holds only for systems ruled by a globally Lipschitz vector field and remains largely open for the input-to-state stability (ISS) property. In this paper, we rely on the notion of exponential ISS to extend the class of systems for which GES or ISS can be concluded from a point-wise dissipation. Our results in turn show that these properties still hold in the presence of a sufficiently small additional term involving the whole state history norm. We provide explicit estimates of the tolerable magnitude of this extra term and show through an example how it can be used to assess robustness with respect to modeling uncertainties.
