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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?

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? Correct Answer Only II is true

Concept:

An LTI system is stable if and only if the ROC of the impulse function H(s) includes the jω axis.

For Causal System → ROC is to the right side of the rightmost pole.

For Anti Causal System → ROC is to the left side of the left-most pole.

Observations:

  • For a causal system to be stable, the poles must lie on the left half of the complex plane (to include the jω axis)
  • A causal system with a pole on the right side cannot be BIBO stable because it's ROC can never include the jω axis. (Statement (II) is therefore correct)
  • A BIBO system with a pole in the right half of the complex plane is stable if the system is anti-causal, as this will include the jω axis. (Statement (I) is therefore incorrect)

Related Questions

Consider the following statements for continuous-time linear time invariant (LTI) systems.
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2. 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?
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Signal Processing mcq question image
Where h(t) is shown in the graph
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P3 : Linear and time-invariant
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