In this paper, we are concerned with almost periodic sequences. We study various types of almost periodic sequences arising in the literature and adapt their notions to the parametric framework. Then, similarly to the continuous case, we aim to prove variational principles. These variational principles are used to obtain some structural results and some theorems of existence in a Hilbert framework. We give, in particular, a discrete version of Amerio's criterion, and adapt a known method to the discrete time case in order to get an existence result on Hilbert space. The condition we obtain allows to find a classical known condition in the case where the system is linear with constant coefficients.

在本文中，我们关注的是几乎周期性的序列。我们研究了文献中出现的各种类型的几乎周期性的序列，并将它们的概念适应参数框架。然后，类似于连续情况，我们旨在证明变分原理。这些变分原理用于在希尔伯特框架中获得一些结构结果和一些存在定理。我们特别给出了 Amerio 准则的离散版本，并将已知方法应用于离散时间情况，以获得希尔伯特空间上的存在结果。我们获得的条件允许在系统是具有常数系数的线性的情况下找到经典的已知条件。