Inspired by the work of Tsiamis et al. \cite{tsiamis2022learning}, in this
paper we study the statistical hardness of learning to stabilize linear
time-invariant systems. Hardness is measured by the number of samples required
to achieve a learning task with a given probability. The work in
\cite{tsiamis2022learning} shows that there exist system classes that are hard
to learn to stabilize with the core reason being the hardness of
identification. Here we present a class of systems that can be easy to
identify, thanks to a non-degenerate noise process that excites all modes, but
the sample complexity of stabilization still increases exponentially with the
system dimension. We tie this result to the hardness of co-stabilizability for
this class of systems using ideas from robust control.

通过对 Tsiamis 等人的工作进行启发，本文研究了学习线性时不变系统的统计困难性，难度通过实现给定概率下所需样本数来衡量；作者通过展示一类系统可以容易地进行识别，但系统稳定化的样本复杂度仍然随系统维度呈指数增加，并利用强控制中的理念将此结果与该系统类别的共稳定性困难性相关联。