Forums

Stability from laplace transform analysis

Started by dhaval_shah January 13, 2010
All,

Can any one pls explain me how "sigma" in s in laplace transform > 0 means
un-stable system and < 0 means stable system?

My understanding is completely reverse to that.

BR,
Dhaval


On 13 Jan, 13:52, "dhaval_shah" <shah.dhavals...@gmail.com> wrote:
> All, > > Can any one pls explain me how "sigma" in s in laplace transform > 0 means > un-stable system and < 0 means stable system? > > My understanding is completely reverse to that.
The Laplace Transform contains an exponential term exp(+/-s) where s = sigma + jw. Depending on the choise of sign in that exponent, the sigma term corresponds to a time domain term that either grows or decays exponentially with increasing time. The *conventional* *choise* of signs is such that sigma < 0 corresponds to an exponentially decaying term in time domain. Rune