Linear time invariant(LTI) systems

[JohnielWhite]

Good day everyone. Could someone please explain what is meant by a linear time invariant(LTI) system?
From what I have read on linear and time invariant systems separately. I would assume that a LTI system is one that obeys the principles of superposition and a shift in input causes a corresponding shift in output. Could some confirm this or correct it because I don't want to have the wrong concept of LTI systems.
Thanks in advance.

 

[viscousflow]

Any linear system obeys the law of superposition. An LTI system has the form:

$$\dot{x}=Ax+Bu$$
$$y=Cx+Du$$

But you can add effects such as input noise and process noise in the following manner:

$$\dot{x}=Ax+Bu+Hv$$
$$y=Cx+Du+Gw$$

Where $$v$$ and $$w$$ are input and process noise respectively.

And yes, a shift in input does cause a corresponding shift in output.

 

[JohnielWhite]

Thanks for the clarification viscousflow.