The term "linear system" usually means some kind of filter which takes an input signal and produces an output signal. Such a filter is linear if it obeys the superposition principle: two summed inputs produces an output that's equal to the two inputs passed independently through the filter, and then summed afterwards.
In any event, a "linear system" may have some memory, usually used to add present samples of the input to past samples of the input. In this sense, you may store information in such a system, though, if you keep applying inputs, your data will eventually be lost.
Note: since this has nothing to do with astronomy, I'm moving it to general engineering.
- Warren