AI 中文总结
研究受外部干扰和无限历史记忆影响的Timoshenko方程在iISS框架下的鲁棒性，通过状态范数给出严格PiISS定义，推导其及EiISS的充分条件，利用相关理论建立适定性并评估，刻画干扰和记忆对系统稳定性的影响。
AI 中文摘要
本文在积分输入到状态稳定性（iISS）框架下研究了受外部干扰和无限历史记忆影响的Timoshenko方程的鲁棒性。多项式iISS（PiISS）是刻画这两个因素影响的有力工具，但现有PiISS定义依赖状态图范数，与无限维系统经典iISS概念不一致。本文仅通过状态范数为一类Timoshenko方程提供了严格的PiISS定义，在松弛函数的Tolksdorf条件下推导了PiISS的充分条件，在更强条件下推导了指数iISS（EiISS）。利用半群和椭圆方程理论建立了适定性。通过构造适当的Lyapunov泛函并采用各种解的先验估计来评估PiISS和EiISS，从而充分刻画了干扰和历史记忆对系统稳定性的影响。
英文摘要
This paper investigates the robustness of Timoshenko equations subject to external disturbances and infinite history memory within the integral input-to-state stability (iISS) framework. While polynomial iISS (PiISS) is a powerful tool for characterizing the influence of these two factors, the existing definitions of PiISS rely on graph norms of the state, which are inconsistent with the classical iISS notion for infinite-dimensional systems. In this paper, we provide a rigorous PiISS definition for a class of Timoshenko equations solely via the state norm, and derive sufficient conditions for PiISS under the Tolksdorf condition on the relaxation function, as well as exponential iISS (EiISS) under a stronger condition. The well-posedness is established by using the semigroup and elliptic equation theories. The PiISS and EiISS are assessed by constructing appropriate Lyapunov functionals and employing various a priori estimates of solutions, thereby fully characterizing the impact of disturbances and history memory on system stability.
