Theoretically a time invariant system can be defined as the system in which the output shifts with the shift in input, the characteristics of output won't change but there will be only shift with input.
But practically it is not easy to find a time invariant system as the characteristics of any system changes with time.
Let us take a electric motor, With the input as current or voltage. It is expected to behave same all the time with input irrespective of time. But because of wear and tear of machine, the mechanical power generated by motor may vary with usage. So you cant consider this as a time invariant system.
But if you consider the same machine as ideal machine, then friction wont exist and the motor should give the same output irrespective of time making the system time invariant.
What if we want to have a time invariant system in non-ideally. this can be near archived as follows.
Let us consider we have a camera and we are trying to take a picture of wall. Here we can take the picture at any time but the picture is not going to change if the wall is left untouched. So this system can be considered as time invariant system to some extent.
From these examples, we can try to redefine time invariant system in another manner as follows
"A time invariant system is a system in which the input domain is not in time." i.e., the characteristics of system doesn't change with time.
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