what is the meaning of a relaxed system?

[tanyeun]

I saw some books talked about relaxed LTI system
I don't know what's that mean by relaxed?

what's that mean a system is initial at rest?
is it the same idea?

thx,

David

 

[kalyanram]

Hi David,

Relaxed and initial rest are one and the same. When modelling a system through differential equations (assuming a continuous time case) we conclude that this system is LTI if and only if y(0)=0 as well as yn(0)=0. Where yn(0) is the nth derivative of the output at t=0 ,in the nth order differential equation describing the system.

Hence relaxed or initial rest is an imperative criteria for LTI.

Hope that clarifies things.

Regards,
~Kalyan