We study admissible observation operators for perturbed evolution equations using the concept of maximal regularity. We first show the invariance of the maximal \(L^p\)-regularity under non-autonomous Miyadera–Voigt perturbations. Second, we establish the invariance of admissibility of observation operators under such a class of perturbations. Finally, we illustrate our result with two examples, one on a non-autonomous parabolic system, and the other on an evolution equation subject to a Neumann boundary condition and a non local perturbation.

中文翻译：

---

论最大规律性背景下观测算子的可接受性

我们使用最大正则性的概念研究摄动演化方程的可接受观测算子。我们首先展示非自治 Miyadera-Voigt 扰动下最大\(L^p\) 正则性的不变性。其次，我们建立了在此类扰动下观测算子的可接受性的不变性。最后，我们用两个例子来说明我们的结果，一个是非自治抛物线系统，另一个是受诺伊曼边界条件和非局部扰动影响的演化方程。