This paper considers robustness for linear evolution equations with non-instantaneous impulsive effects in Banach spaces. We present sufficient conditions to guarantee robustness of nonuniform exponential contractions and exponential dichotomies with both non-instantaneous linear impulsive actions of the associated equation and linear perturbations of the associated linear evolution equation. This paper establishes a new framework to investigate robustness for linear evolution equations with non-instantaneous impulsive conditions and also generalizes results from classical impulsive equations using several nontrivial techniques.

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具有非瞬时脉冲效应的线性发展方程的鲁棒性

本文考虑Banach空间中具有非瞬时脉冲效应的线性发展方程的鲁棒性。我们提出了充分的条件，以保证非均匀指数收缩和指数二分法的健壮性，同时具有相关联方程的非瞬时线性脉冲作用和相关线性演化方程的线性摄动。本文建立了一个新的框架，以研究具有非瞬时脉冲条件的线性发展方程的鲁棒性，并利用几种非平凡的技术对经典脉冲方程的结果进行了推广。