Hi, I've been given the following question for homework.
Determine if the following characteristic equation represents a stable or unstable system.
$\displaystyle s^3+6s^2+11s+6=0$
Any tips in solving this would be of great help.
Thanks
Hi, I've been given the following question for homework.
Determine if the following characteristic equation represents a stable or unstable system.
$\displaystyle s^3+6s^2+11s+6=0$
Any tips in solving this would be of great help.
Thanks
Hi there
I found one zero by guessing, it is s=-1. (I know, this is very disappointing, but very fast compared with other methods like http://en.wikipedia.org/wiki/Newton%27s_method or http://en.wikipedia.org/wiki/Cubic_f...ano.27s_method)
Using polynomial long division leads to
$\displaystyle (s^3+6s^2+11s+6)/(s-(-1)) $
$\displaystyle = s^2 + 5s + 6$
You should be able to find the other two zeros, -3 and -2
All zeros are < 0, therfor I guess (but I don't know) it represents a stable system.
Cheers
Rapha