Poles and Zeros of a Dynamic System

General Map

Worked Examples:

i) Zeros at $s=-4$ Poles at $s^2+3s+2=0$, $(s+2)(s+1)=0$, $s=-2,s=-1$

All are negative, and real, therefore the system is stable and not oscillatory

ii) Zeros at $s=-5$ Poles at $(s+3)(s-2)=0,s=-3,s=2$

The system is not oscillatory but is unstable

iii) Zeros at $s=-3,s=-2$ Poles at $s=-1$ This system is stable, experiencing exponential decay and not oscillatory