Memory in a System
Memoryless System
A system has memory only if it depends on current input with no offset.
Example:
$ y(t)=\frac{1}{2}x(t)+1 $
In the above example, the output only depends on the current time, $ t $.
System with Memory
Conversely, a system with memory must depend on input from some time in the past or future. It can depend on current input as long as it also depends on some past or future time.
Example:
$ y(t)=\frac{1}{2}x(t+1) $
In the above example, the output depends on a time in the future, $ t+1 $.
