Question

Say we have a transfer function that is H(s)= (2s^2-5s+3) / (s-1). Which of these statements is correct?

This system is stable, since one of its zeros is in the right-hand part of the s-plane

This system is stable, since one of its poles is in the right-hand part of the s-plane

This system is unstable, since its only zero is in the left-hand part of the s-plane

This system is stable, since its only pole is in the left-hand part of the s-plane

This system is stable, since one of its zeros is in the left-hand part of the s-plane

This system is unstable, since one of its poles is in the right-hand part of the s-plane

This system is stable, since its only zero is in the left-hand part of the s-plane

This system is unstable, since its only pole is in the right-hand part of the s-plane

All other answers are incorrect

Answer 1

4.This system is stable, since its only pole is in the left-hand part of the s-plane

Poles of Transfer function are solely responsible for the system stability. If the poles are in Left Half of S Plane the system is BIBO Stable.

If atleast one pole in Right Half of S plane the system is said to be unstable. Since the system response is no more bounded to a bounded input due to the presence of a continuosly increasing exponential in the output term

and If the system has simple poles on the imaginary axis then it is said to be marginally or conditionally stable. that is conditional/ subjected to the inputs it may said to be stable system. if the system has double poles on imaginary axis, it is unstable (due to the ramp term coming in the response.)

Now the given Transfer function H(s)= (2s^2-5s+3) / (s-1) has two zeroes and 1 pole. Clearly we are concerned about pole regarding stability. So since pole in in Left half of S plane S=-1 thus the system is Bounded input Bounded Output Stable.

Hence This system is stable, since its only pole is in the left-hand part of the s-plane is the correct statement