Can I determine a system's $z$-domain transfer function from its pole-zero plot?

1. Is it possible to plot the pole-zero using Z transform?
2. What does pole-zero plot tell us?
3. How do you know if a system is stable from a pole-zero plot?

Is it possible to plot the pole-zero using Z transform?

Once the poles and zeros have been found for a given Z-Transform, they can be plotted onto the Z-Plane.

What does pole-zero plot tell us?

A pole-zero plot shows the location in the complex plane of the poles and zeros of the transfer function of a dynamic system, such as a controller, compensator, sensor, equalizer, filter, or communications channel.

How do you know if a system is stable from a pole-zero plot?

If all the poles lie in the left half of the s-plane, then the system is stable. If the system has two or more poles in the same location on the imaginary axis, then the system is unstable. If the system has one or more non-repeated poles on the imaginary axis, then the system is marginally stable.