# Time invariance

#### EEnOOb

Joined Oct 7, 2005
3
Not really a homework question but it's a rather basic one so I figured this would be the place to post it. It seems to me that any continuous time system in which the output depends on some time-derivative of the output (i.e. y(t) = x(t) + dy(t)/dt) cannot possibly be a time-invariant system. Am I correct in this assumption or am I missing something important?

Joined Jan 19, 2004
220
a invariant system i think should be of the form y(t)=constant

#### EEnOOb

Joined Oct 7, 2005
3
Originally posted by haditya@Oct 7 2005, 09:13 PM
a invariant system i think should be of the form y(t)=constant
[post=10865]Quoted post[/post]​
A time invariant system is one where y(x(t),t-T)=y(x(t-T),t). In other words, a shift of T in the input signal causes a corresponding shift by T of the output signal. If my initial guess was correct then any continuous-time circuit with a capacitor or an inductor in it would not be time-invariant. I'm pretty sure that this is not the case but I can't seem to figure out the math to prove it. In fact when I do the math I can only disprove the time-invariance of a capacitor or inductor system. I must be doing something wrong but I can't figure out what it is.

#### EEnOOb

Joined Oct 7, 2005
3
Nevermind, I figured out why my math wasn't coming out right. I understand this now.