The GATE Grind

GATE 2017 EC – Question 15

Networks, Signals and Systems · LTI Systems · 1 mark · Multiple choice

Consider the following statements for continuous-time linear time invariant (LTI) systems.

I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.

II. There is no causal and BIBO stable system with a pole in the right half of the complex plane.

Which one among the following is correct?

  1. Both I and II are true
  2. Both I and II are not true
  3. Only I is true
  4. Only II is true

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) Only II is true

Explanation

A causal system is stable only if all its poles are in the left half plane, so II is true. A non-causal system can have a pole in the right half plane and still be stable, when its region of convergence is chosen to include the imaginary axis, so I is false.