Find out if the system is linear and time-invariant

1. How do you know if a system is linear and time invariant?
2. How do I know if my system is time variant or not?
3. Which system is time invariant?

How do you know if a system is linear and time invariant?

One test to verify time invariance/variance property of a system is to shift the response of the system to an input signal and apply a shifted input, to the same system and compare the two waveforms, so obtained. If the system is time invariant, the two waveforms will match when the input and output shifts match.

How do I know if my system is time variant or not?

To assess whether a system is time-varying or not, follow these steps: replace u(t) with u(t−τ) on one side of the equation, replace y(t) with y(t−τ) on the other side of the equation, and then check if they are equal.

Which system is time invariant?

In control theory, a time-invariant (TIV) system has a time-dependent system function that is not a direct function of time. Such systems are regarded as a class of systems in the field of system analysis. The time-dependent system function is a function of the time-dependent input function.