From what I know about root locus is that if all roots are located on the Left Half of the S-plane the system is stable. That's why I expected the unit step response of a system to be stable.
Transfer function: $$ G(s) = \frac{1+s}{s(s+1)^{2}} $$
After I plotted the locus and step response in Matlab, I got stuck.

enter image description here

Matlab code:

sys = tf([1 1], [1 2 1 0]);

s = tf('s');
GH = (1 + s) / (s*(s+1)^2);

1 Answer 1


The root locus is all the possible roots of a closed loop system that has an open loop transfer function $k G(s)$, when the gain is varied in the range $k \in (0, \infty)$ then $G(s)$, itself, does not have to be stable.

Try it again, only in closed loop with an open-loop gain of $\frac 2 9 G(s)$.


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