Abstract This paper deals with the exponential input-to-state stabilization with respect to boundary disturbances of a class of diagonal infinite-dimensional systems via delay boundary control. The considered input delays are uncertain and time-varying. The proposed control strategy consists of a constant-delay predictor feedback controller designed on a truncated finite-dimensional model capturing the unstable modes of the original infinite-dimensional system. We show that the resulting closed-loop system is exponentially input-to-state stable with fading memory of both additive boundary input perturbations and disturbances in the computation of the predictor feedback.

中文翻译：

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一类带延迟边界控制的对角边界控制系统的指数输入状态稳定

摘要 本文通过延迟边界控制处理一类对角无限维系统边界扰动下的指数输入到状态镇定。所考虑的输入延迟是不确定且随时间变化的。所提出的控制策略包括在截断有限维模型上设计的恒定延迟预测器反馈控制器，该模型捕获原始无限维系统的不稳定模式。我们表明，由此产生的闭环系统是指数输入到状态稳定的，并且在预测器反馈的计算中对加性边界输入扰动和扰动的记忆逐渐消失。